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Condensed matter physics is the field of
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
that deals with the macroscopic and microscopic physical properties of
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
, especially the
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
and
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
phases which arise from
electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
forces between
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the
superconducting Superconductivity is a set of physical properties observed in certain materials where Electrical resistance and conductance, electrical resistance vanishes and magnetic field, magnetic flux fields are expelled from the material. Any material e ...
phase exhibited by certain materials at low
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
, the
ferromagnet Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...
ic and
antiferromagnet In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...
ic phases of
spins The spins (as in having "the spins")Diane Marie Leiva. ''The Florida State University College of Education''Women's Voices on College Drinking: The First-Year College Experience"/ref> is an adverse reaction of intoxication that causes a state of v ...
on
crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
s of atoms, and the
Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67&n ...
found in
ultracold atom Ultracold atoms are atoms that are maintained at temperatures close to 0 kelvin (absolute zero), typically below several tens of microkelvin (µK). At these temperatures the atom's quantum-mechanical properties become important. To reach such low ...
ic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the
physical law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) a ...
s of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
,
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
,
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
, and other
theories A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...
to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists, and the Division of Condensed Matter Physics is the largest division at the
American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...
. The field overlaps with
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, materials science,
engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
and
nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal o ...
, and relates closely to
atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
and
biophysics Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. ...
. The
theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
of condensed matter shares important concepts and methods with that of
particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
and
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the ...
. A variety of topics in physics such as
crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...
,
metallurgy Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the sc ...
,
elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...
,
magnetism Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
, etc., were treated as distinct areas until the 1940s, when they were grouped together as ''
solid-state physics Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the l ...
''. Around the 1960s, the study of physical properties of
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
s was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics. The
Bell Telephone Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mul ...
was one of the first institutes to conduct a research program in condensed matter physics. According to founding director of the
Max Planck Institute for Solid State Research The Max Planck Institute for Solid State Research (German: ''Max-Planck-Institut für Festkörperforschung'') was founded in 1969 and is one of the 82 Max Planck Institutes of the Max Planck Society. It is located on a campus in Stuttgart, togeth ...
, physics professor Manuel Cardona, it was
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
who created the modern field of condensed matter physics starting with his seminal 1905 article on the
photoelectric effect The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid st ...
and
photoluminescence Photoluminescence (abbreviated as PL) is light emission from any form of matter after the absorption of photons (electromagnetic radiation). It is one of many forms of luminescence (light emission) and is initiated by photoexcitation (i.e. photon ...
which opened the fields of
photoelectron spectroscopy Photoemission spectroscopy (PES), also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in th ...
and
photoluminescence spectroscopy Photoluminescence (abbreviated as PL) is light emission from any form of matter after the absorption of photons (electromagnetic radiation). It is one of many forms of luminescence (light emission) and is initiated by photoexcitation (i.e. photon ...
, and later his 1907 article on the
specific heat of solids Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity ...
which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the specific heat. Deputy Director of the Yale Quantum Institute
A. Douglas Stone A. Douglas Stone is the Carl Morse Professor of Applied Physics and Physics at Yale University. He was the 2014 recipient of the Phi Beta Kappa Award in Science for his book ''Einstein and the Quantum: The Quest of the Valiant Swabian''. He has a ...
makes a similar priority case for Einstein in his work on the synthetic history of quantum mechanics.


Etymology

According to physicist
Philip Warren Anderson Philip Warren Anderson (December 13, 1923 – March 29, 2020) was an American theoretical physicist and Nobel laureate. Anderson made contributions to the theories of localization, antiferromagnetism, symmetry breaking (including a paper in 19 ...
, the use of the term "condensed matter" to designate a field of study was coined by him and
Volker Heine Volker Heine FRS (born 19 September 1930 in Hamburg, Germany) is a New Zealand / British physicist. He is married to Daphne and they have three children. Volker Heine is considered a pioneer of theoretical and computational studies of the electr ...
, when they changed the name of their group at the
Cavendish Laboratories The Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the School of Physical Sciences. The laboratory was opened in 1874 on the New Museums Site as a laboratory for experimental physics and is named ...
,
Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...
from ''Solid state theory'' to ''Theory of Condensed Matter'' in 1967, as they felt it better included their interest in liquids,
nuclear matter Nuclear matter is an idealized system of interacting nucleons ( protons and neutrons) that exists in several phases of exotic matter that, as of yet, are not fully established. It is ''not'' matter in an atomic nucleus, but a hypothetical s ...
, and so on. Although Anderson and Heine helped popularize the name "condensed matter", it had been used in Europe for some years, most prominently in the
Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...
journal ''Physics of Condensed Matter'', launched in 1963. The name "condensed matter physics" emphasized the commonality of scientific problems encountered by physicists working on solids, liquids, plasmas, and other complex matter, whereas "solid state physics" was often associated with restricted industrial applications of metals and semiconductors. In the 1960s and 70s, some physicists felt the more comprehensive name better fit the funding environment and
Cold War The Cold War is a term commonly used to refer to a period of geopolitical tension between the United States and the Soviet Union and their respective allies, the Western Bloc and the Eastern Bloc. The term '' cold war'' is used because the ...
politics of the time. References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 book ''Kinetic Theory of Liquids'',
Yakov Frenkel __NOTOC__ Yakov Il'ich Frenkel (russian: Яков Ильич Френкель; 10 February 1894 – 23 January 1952) was a Soviet physicist renowned for his works in the field of condensed matter physics. He is also known as Jacov Frenkel, frequ ...
proposed that "The kinetic theory of liquids must accordingly be developed as a generalization and extension of the kinetic theory of solid bodies. As a matter of fact, it would be more correct to unify them under the title of 'condensed bodies'".


History of condensed matter physics


Classical physics

One of the first studies of condensed states of matter was by
English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...
chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe th ...
Humphry Davy Sir Humphry Davy, 1st Baronet, (17 December 177829 May 1829) was a British chemist and inventor who invented the Davy lamp and a very early form of arc lamp. He is also remembered for isolating, by using electricity, several elements for t ...
, in the first decades of the nineteenth century. Davy observed that of the forty
chemical element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
s known at the time, twenty-six had
metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
lic properties such as
lustre Lustre or Luster may refer to: Places * Luster, Norway, a municipality in Vestlandet, Norway ** Luster (village), a village in the municipality of Luster * Lustre, Montana, an unincorporated community in the United States Entertainment * '' ...
,
ductility Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile stres ...
and high electrical and thermal conductivity. This indicated that the atoms in
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into colour blindness, which he had. Colour b ...
's
atomic theory Atomic theory is the scientific theory that matter is composed of particles called atoms. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter a ...
were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as
nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...
and
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
could be liquefied under the right conditions and would then behave as metals. In 1823,
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
, then an assistant in Davy's lab, successfully liquefied
chlorine Chlorine is a chemical element with the Symbol (chemistry), symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate betwee ...
and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
. Shortly after, in 1869,
Irish Irish may refer to: Common meanings * Someone or something of, from, or related to: ** Ireland, an island situated off the north-western coast of continental Europe ***Éire, Irish language name for the isle ** Northern Ireland, a constituent unit ...
chemist
Thomas Andrews Thomas Andrews Jr. (7 February 1873 – 15 April 1912) was a British businessman and shipbuilder. He was managing director and head of the drafting department of the shipbuilding company Harland and Wolff in Belfast, Ireland. He was the nava ...
studied the
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
from a liquid to a gas and coined the term critical point to describe the condition where a gas and a liquid were indistinguishable as phases, and
Dutch Dutch commonly refers to: * Something of, from, or related to the Netherlands * Dutch people () * Dutch language () Dutch may also refer to: Places * Dutch, West Virginia, a community in the United States * Pennsylvania Dutch Country People E ...
physicist
Johannes van der Waals Johannes Diderik van der Waals (; 23 November 1837 – 8 March 1923) was a Dutch theoretical physics, theoretical physicist and thermodynamicist famous for his pioneering work on the equation of state for gases and liquids. Van der Waals starte ...
supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures. By 1908,
James Dewar Sir James Dewar (20 September 1842 – 27 March 1923) was a British chemist and physicist. He is best known for his invention of the vacuum flask, which he used in conjunction with research into the liquefaction of gases. He also studied ato ...
and
Heike Kamerlingh Onnes Heike Kamerlingh Onnes (21 September 1853 – 21 February 1926) was a Dutch physicist and Nobel laureate. He exploited the Hampson–Linde cycle to investigate how materials behave when cooled to nearly absolute zero and later to liquefy helium f ...
were successfully able to liquefy hydrogen and then newly discovered
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
, respectively.
Paul Drude Paul Karl Ludwig Drude (; 12 July 1863 – 5 July 1906) was a German physicist specializing in optics. He wrote a fundamental textbook integrating optics with Maxwell's theories of electromagnetism. Education Born into an ethnic German family, D ...
in 1900 proposed the first theoretical model for a classical
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
moving through a metallic solid. Drude's model described properties of metals in terms of a gas of free electrons, and was the first microscopic model to explain empirical observations such as the
Wiedemann–Franz law In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (''κ'') to the electrical conductivity (''σ'') of a metal is proportional to the temperature (''T''). : \frac \kappa ...
. However, despite the success of Drude's free electron model, it had one notable problem: it was unable to correctly explain the electronic contribution to the
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures. In 1911, three years after helium was first liquefied, Onnes working at
University of Leiden Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of Le ...
discovered
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
in
mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value. The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
, in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."


Advent of quantum mechanics

Drude's classical model was augmented by
Wolfgang Pauli Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics fo ...
,
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretica ...
,
Felix Bloch Felix Bloch (23 October 1905 – 10 September 1983) was a Swiss-American physicist and Nobel physics laureate who worked mainly in the U.S. He and Edward Mills Purcell were awarded the 1952 Nobel Prize for Physics for "their development of ne ...
and other physicists. Pauli realized that the free electrons in metal must obey the
Fermi–Dirac statistics Fermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac di ...
. Using this idea, he developed the theory of
paramagnetism Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, ...
in 1926. Shortly after, Sommerfeld incorporated the
Fermi–Dirac statistics Fermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac di ...
into the free electron model and made it better to explain the heat capacity. Two years later, Bloch used
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
to describe the motion of an electron in a periodic lattice. The mathematics of crystal structures developed by
Auguste Bravais Auguste Bravais (; 23 August 1811, Annonay, Ardèche – 30 March 1863, Le Chesnay, France) was a French physicist known for his work in crystallography, the conception of Bravais lattices, and the formulation of Bravais law. Bravais also studie ...
,
Yevgraf Fyodorov Evgraf Stepanovich Fedorov (russian: Евгра́ф Степа́нович Фёдоров, – 21 May 1919) was a Russian mathematician, crystallographer and mineralogist. Fedorov was born in the Russian city of Orenburg. His father was a topo ...
and others was used to classify crystals by their
symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient ...
, and tables of crystal structures were the basis for the series ''International Tables of Crystallography'', first published in 1935. Band structure calculations was first used in 1930 to predict the properties of new materials, and in 1947
John Bardeen John Bardeen (; May 23, 1908 – January 30, 1991) was an American physicist and engineer. He is the only person to be awarded the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the tran ...
,
Walter Brattain Walter Houser Brattain (; February 10, 1902 – October 13, 1987) was an American physicist at Bell Labs who, along with fellow scientists John Bardeen and William Shockley, invented the point-contact transistor in December 1947. They shared the ...
and
William Shockley William Bradford Shockley Jr. (February 13, 1910 – August 12, 1989) was an American physicist and inventor. He was the manager of a research group at Bell Labs that included John Bardeen and Walter Brattain. The three scientists were jointly ...
developed the first
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
-based
transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
, heralding a revolution in electronics. In 1879,
Edwin Herbert Hall Edwin Herbert Hall (November 7, 1855 – November 20, 1938) was an American physicist, who discovered the eponymous Hall effect. Hall conducted thermoelectric research and also wrote numerous physics textbooks and laboratory manuals. Biograp ...
working at the
Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hem ...
discovered a voltage developed across conductors transverse to an electric current in the conductor and magnetic field perpendicular to the current. This phenomenon arising due to the nature of charge carriers in the conductor came to be termed the
Hall effect The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. It was disco ...
, but it was not properly explained at the time, since the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics,
Lev Landau Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His a ...
in 1930 developed the theory of
Landau quantization In quantum mechanics, Landau quantization refers to the quantization of the cyclotron orbits of charged particles in a uniform magnetic field. As a result, the charged particles can only occupy orbits with discrete, equidistant energy values, call ...
and laid the foundation for the theoretical explanation for the
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exh ...
discovered half a century later. Magnetism as a property of matter has been known in China since 4000 BC. However, the first modern studies of magnetism only started with the development of
electrodynamics In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
by Faraday, Maxwell and others in the nineteenth century, which included classifying materials as
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
and
diamagnetic Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted ...
based on their response to magnetization.
Pierre Curie Pierre Curie ( , ; 15 May 1859 – 19 April 1906) was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity, and radioactivity. In 1903, he received the Nobel Prize in Physics with his wife, Marie Curie, and Henri Becqu ...
studied the dependence of magnetization on temperature and discovered the
Curie point In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
phase transition in ferromagnetic materials. In 1906,
Pierre Weiss Pierre-Ernest Weiss (25 March 1865, Mulhouse – 24 October 1940, Lyon) was a French physicist who specialized in magnetism. He developed the Magnetic domain, domain theory of ferromagnetism in 1907. Magnetic domain, Weiss domains and the Weiss ...
introduced the concept of
magnetic domain A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. When c ...
s to explain the main properties of ferromagnets. The first attempt at a microscopic description of magnetism was by
Wilhelm Lenz Wilhelm Lenz (February 8, 1888 in Frankfurt am Main – April 30, 1957 in Hamburg) was a German physicist, most notable for his invention of the Ising model and for his application of the Laplace–Runge–Lenz vector to the old quantum mechanical ...
and
Ernst Ising Ernst Ising (; May 10, 1900 in Cologne, Germany – May 11, 1998 in Peoria, Illinois, USA) was a German physicist, who is best remembered for the development of the Ising model. He was a professor of physics at Bradley University until his r ...
through the
Ising model The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent ...
that described magnetic materials as consisting of a periodic lattice of
spins The spins (as in having "the spins")Diane Marie Leiva. ''The Florida State University College of Education''Women's Voices on College Drinking: The First-Year College Experience"/ref> is an adverse reaction of intoxication that causes a state of v ...
that collectively acquired magnetization. The Ising model was solved exactly to show that
spontaneous magnetization Spontaneous magnetization is the appearance of an ordered spin state (magnetization) at zero applied magnetic field in a ferromagnetic or ferrimagnetic material below a critical point called the Curie temperature or . Overview Heated to temperat ...
cannot occur in one dimension but is possible in higher-dimensional lattices. Further research such as by Bloch on
spin wave A spin wave is a propagating disturbance in the ordering of a magnetic material. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as ...
s and Néel on
antiferromagnetism In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...
led to developing new magnetic materials with applications to
magnetic storage Magnetic storage or magnetic recording is the storage of data on a magnetized medium. Magnetic storage uses different patterns of magnetisation in a magnetizable material to store data and is a form of non-volatile memory. The information is acc ...
devices.


Modern many-body physics

The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
and the
Kondo effect In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature. The cause of the effect was fir ...
. After
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, several ideas from quantum field theory were applied to condensed matter problems. These included recognition of
collective excitation In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
modes of solids and the important notion of a quasiparticle. Russian physicist
Lev Landau Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His a ...
used the idea for the
Fermi liquid theory Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interactions among the particles of the many-body ...
wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles. Landau also developed a
mean-field theory In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...
for continuous phase transitions, which described ordered phases as spontaneous breakdown of symmetry. The theory also introduced the notion of an
order parameter In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
to distinguish between ordered phases. Eventually in 1956,
John Bardeen John Bardeen (; May 23, 1908 – January 30, 1991) was an American physicist and engineer. He is the only person to be awarded the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the tran ...
,
Leon Cooper Leon N Cooper (born February 28, 1930) is an American physicist and Nobel Prize laureate who, with John Bardeen and John Robert Schrieffer, developed the BCS theory of superconductivity. His name is also associated with the Cooper pair and co-deve ...
and
John Schrieffer John Robert Schrieffer (; May 31, 1931 – July 27, 2019) was an American physicist who, with John Bardeen and Leon Cooper, was a recipient of the 1972 Nobel Prize in Physics for developing the BCS theory, the first successful quantum theo ...
developed the so-called
BCS theory BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes sup ...
of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s in the lattice can give rise to a bound state called a
Cooper pair In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper ...
. The study of phase transitions and the critical behavior of observables, termed
critical phenomena In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations ...
, was a major field of interest in the 1960s.
Leo Kadanoff Leo Philip Kadanoff (January 14, 1937 – October 26, 2015) was an American physicist. He was a professor of physics (emeritus from 2004) at the University of Chicago and a former President of the American Physical Society (APS). He contributed t ...
,
Benjamin Widom Benjamin Widom (born 13 October 1927) is the Goldwin Smith Professor of Chemistry at Cornell University. His research interests include physical chemistry and statistical mechanics. In 1998, Widom was awarded the Boltzmann Medal "for his illumi ...
and
Michael Fisher Michael Ellis Fisher (3 September 1931 – 26 November 2021) was an English physicist, as well as chemist and mathematician, known for his many seminal contributions to statistical physics, including but not restricted to the theory of phase t ...
developed the ideas of
critical exponent Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in ...
s and
widom scaling Widom scaling (after Benjamin Widom) is a hypothesis in statistical mechanics regarding the free energy of a magnetic system near its critical point which leads to the critical exponents becoming no longer independent so that they can be parameter ...
. These ideas were unified by
Kenneth G. Wilson Kenneth Geddes "Ken" Wilson (June 8, 1936 – June 15, 2013) was an American theoretical physicist and a pioneer in leveraging computers for studying particle physics. He was awarded the 1982 Nobel Prize in Physics for his work on phase ...
in 1972, under the formalism of the
renormalization group In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the ...
in the context of quantum field theory. The
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exh ...
was discovered by
Klaus von Klitzing Klaus von Klitzing (, born 28 June 1943, Schroda) is a German physicist, known for discovery of the integer quantum Hall effect, for which he was awarded the 1985 Nobel Prize in Physics. Education In 1962, Klitzing passed the Abitur at the Ar ...
, Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant e^2/h.(see figure) The effect was observed to be independent of parameters such as system size and impurities. In 1981, theorist
Robert Laughlin Robert Betts Laughlin (born November 1, 1950) is the Anne T. and Robert Bass (businessman), Robert M. Bass Professor of Physics and Applied Physics at Stanford University. Along with Horst L. Störmer of Columbia University and Daniel C. Ts ...
proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance is proportional to a topological invariant, called
Chern number In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since found applications in physics, Calabi–Yau m ...
, whose relevance for the band structure of solids was formulated by David J. Thouless and collaborators. Shortly after, in 1982,
Horst Störmer Horst may refer to: Science * Horst (geology), a raised fault block bounded by normal faults or graben People * Horst (given name) * Horst (surname) * ter Horst, Dutch surname * van der Horst, Dutch surname Places Settlements Germany * Horst, ...
and
Daniel Tsui Daniel Chee Tsui (, born February 28, 1939) is a Chinese-born American physicist, Nobel laureate, and the Arthur Legrand Doty Professor of Electrical Engineering, Emeritus, at Princeton University. Tsui's areas of research include electrical prop ...
observed the
fractional quantum Hall effect The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which elec ...
where the conductance was now a rational multiple of the constant e^2/h. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a
variational method The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
solution, named the
Laughlin wavefunction In condensed matter physics, the Laughlin wavefunction pp. 210-213 is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium ...
. The study of topological properties of the fractional Hall effect remains an active field of research. Decades later, the aforementioned topological band theory advanced by David J. Thouless and collaborators was further expanded leading to the discovery of
topological insulator A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an ...
s. In 1986, Karl Müller and
Johannes Bednorz Johannes Georg Bednorz (; born 16 May 1950) is a German physicist who, together with K. Alex Müller, discovered high-temperature superconductivity in ceramics, for which they shared the 1987 Nobel Prize in Physics. Life and work Bednorz was bor ...
discovered the first
high temperature superconductor High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previou ...
, a material which was superconducting at temperatures as high as 50
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
s. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role. A satisfactory theoretical description of high-temperature superconductors is still not known and the field of
strongly correlated material Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions, heavy fermion ...
s continues to be an active research topic. In 2009, David Field and researchers at
Aarhus University Aarhus University ( da, Aarhus Universitet, abbreviated AU) is a public research university with its main campus located in Aarhus, Denmark. It is the second largest and second oldest university in Denmark. The university is part of the Coimbra Gr ...
discovered spontaneous electric fields when creating
prosaic film Prose is a form of written or spoken language that follows the natural flow of speech, uses a language's ordinary grammatical structures, or follows the conventions of formal academic writing. It differs from most traditional poetry, where the f ...
s of various gases. This has more recently expanded to form the research area of
spontelectrics Spontelectrics is a form of solid state thin films A thin film is a layer of material ranging from fractions of a nanometer ( monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process ref ...
. In 2012, several groups released preprints which suggest that
samarium hexaboride Samarium hexaboride (SmB6) is an intermediate-valence compound where samarium is present both as Sm2+ and Sm3+ ions at the ratio 3:7. It belongs to a class of Kondo insulators. At temperatures above 50 K its properties are typical of a Kondo metal ...
has the properties of a
topological insulator A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an ...
in accord with the earlier theoretical predictions. Since samarium hexaboride is an established
Kondo insulator In solid-state physics, Kondo insulators (also referred as Kondo semiconductors and heavy fermion semiconductors) are understood as materials with strongly correlated electrons, that open up a narrow band gap (in the order of 10 meV) at low tem ...
, i.e. a strongly correlated electron material, it is expected that the existence of a topological Dirac surface state in this material would lead to a topological insulator with strong electronic correlations.


Theoretical

Theoretical condensed matter physics involves the use of theoretical models to understand properties of states of matter. These include models to study the electronic properties of solids, such as the
Drude model The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials (especially metals). Basically, Ohm's law was well established and stated that the current ''J'' and voltage ...
, the
band structure In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or '' ...
and the
density functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...
. Theoretical models have also been developed to study the physics of
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
s, such as the
Ginzburg–Landau theory In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
,
critical exponent Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in ...
s and the use of mathematical methods of
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
and the
renormalization group In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the ...
. Modern theoretical studies involve the use of
numerical computation Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
of electronic structure and mathematical tools to understand phenomena such as
high-temperature superconductivity High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previ ...
,
topological phase In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian ge ...
s, and gauge symmetries.


Emergence

Theoretical understanding of condensed matter physics is closely related to the notion of
emergence In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergence ...
, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents. For example, a range of phenomena related to high temperature superconductivity are understood poorly, although the microscopic physics of individual electrons and lattices is well known. Similarly, models of condensed matter systems have been studied where
collective excitation In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
s behave like
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s and
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s, thereby describing
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
as an emergent phenomenon. Emergent properties can also occur at the interface between materials: one example is the
lanthanum aluminate-strontium titanate interface The interface between lanthanum aluminate (LaAlO3) and strontium titanate (SrTiO3) is a notable materials interface because it exhibits properties not found in its constituent materials. Individually, LaAlO3 and SrTiO3 are non-magnetic Insulator ( ...
, where two band-insulators are joined to create conductivity and
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
.


Electronic theory of solids

The metallic state has historically been an important building block for studying properties of solids. The first theoretical description of metals was given by
Paul Drude Paul Karl Ludwig Drude (; 12 July 1863 – 5 July 1906) was a German physicist specializing in optics. He wrote a fundamental textbook integrating optics with Maxwell's theories of electromagnetism. Education Born into an ethnic German family, D ...
in 1900 with the
Drude model The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials (especially metals). Basically, Ohm's law was well established and stated that the current ''J'' and voltage ...
, which explained electrical and thermal properties by describing a metal as an
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
of then-newly discovered
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s. He was able to derive the empirical Wiedemann-Franz law and get results in close agreement with the experiments. This classical model was then improved by
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretica ...
who incorporated the
Fermi–Dirac statistics Fermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac di ...
of electrons and was able to explain the anomalous behavior of the
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
of metals in the
Wiedemann–Franz law In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (''κ'') to the electrical conductivity (''σ'') of a metal is proportional to the temperature (''T''). : \frac \kappa ...
. In 1912, The structure of crystalline solids was studied by
Max von Laue Max Theodor Felix von Laue (; 9 October 1879 – 24 April 1960) was a German physicist who received the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals. In addition to his scientific endeavors with cont ...
and Paul Knipping, when they observed the
X-ray diffraction X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
pattern of crystals, and concluded that crystals get their structure from periodic lattices of atoms. In 1928, Swiss physicist
Felix Bloch Felix Bloch (23 October 1905 – 10 September 1983) was a Swiss-American physicist and Nobel physics laureate who worked mainly in the U.S. He and Edward Mills Purcell were awarded the 1952 Nobel Prize for Physics for "their development of ne ...
provided a wave function solution to the
Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...
with a periodic potential, known as
Bloch's theorem In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential take the form of a plane wave modulated by a periodic function. The theorem is named after the physicist Felix Bloch, who d ...
. Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions. The Thomas–Fermi theory, developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a variational parameter. Later in the 1930s,
Douglas Hartree Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the c ...
,
Vladimir Fock Vladimir Aleksandrovich Fock (or Fok; russian: Влади́мир Алекса́ндрович Фок) (December 22, 1898 – December 27, 1974) was a Soviet Union, Soviet physicist, who did foundational work on quantum mechanics and quantum ...
and
John Slater John Slater may refer to: Business and government *John Slater (industrialist) (1776–1843), (American) father of John Fox Slater, brother and partner of Samuel Slater *John Fox Slater (1815–1884), American philanthropist, son of John Slater ( ...
developed the so-called Hartree–Fock wavefunction as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for exchange statistics of single particle electron wavefunctions. In general, it is very difficult to solve the Hartree–Fock equation. Only the free electron gas case can be solved exactly. Finally in 1964–65,
Walter Kohn Walter Kohn (; March 9, 1923 – April 19, 2016) was an Austrian-American theoretical physicist and theoretical chemist. He was awarded, with John Pople, the Nobel Prize in Chemistry in 1998. The award recognized their contributions to the unde ...
,
Pierre Hohenberg Pierre C. Hohenberg (3 October 1934 – 15 December 2017) was a French-American theoretical physicist, who worked primarily on statistical mechanics. Hohenberg studied at Harvard, where he earned his bachelor's degree in 1956 and a master's degr ...
and
Lu Jeu Sham Lu Jeu Sham (Chinese: 沈呂九) (born April 28, 1938) is an American physicist. He is best known for his work with Walter Kohn on the Kohn–Sham equations. Biography Lu Jeu Sham's family was from Fuzhou, Fujian, but he was born in British Hong ...
proposed the
density functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...
(DFT) which gave realistic descriptions for bulk and surface properties of metals. The density functional theory has been widely used since the 1970s for band structure calculations of variety of solids.


Symmetry breaking

Some states of matter exhibit ''symmetry breaking'', where the relevant laws of physics possess some form of
symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
that is broken. A common example is
crystalline solid A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...
s, which break continuous
translational symmetry In geometry, to translate a geometric figure is to move it from one place to another without rotating it. A translation "slides" a thing by . In physics and mathematics, continuous translational symmetry is the invariance of a system of equatio ...
. Other examples include magnetized
ferromagnets Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...
, which break
rotational symmetry Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which i ...
, and more exotic states such as the ground state of a BCS superconductor, that breaks
U(1) In mathematics, the circle group, denoted by \mathbb T or \mathbb S^1, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers. \mathbb T = \. ...
phase rotational symmetry.
Goldstone's theorem In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu in parti ...
in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s. For example, in crystalline solids, these correspond to
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s, which are quantized versions of lattice vibrations.


Phase transition

Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
. Classical phase transition occurs at finite temperature when the order of the system was destroyed. For example, when ice melts and becomes water, the ordered crystal structure is destroyed. In
quantum phase transition In physics, a quantum phase transition (QPT) is a phase transition between different quantum phases (phases of matter at zero temperature). Contrary to classical phase transitions, quantum phase transitions can only be accessed by varying a physic ...
s, the temperature is set to
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
, and the non-thermal control parameter, such as pressure or magnetic field, causes the phase transitions when order is destroyed by
quantum fluctuation In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. ...
s originating from the
Heisenberg uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
. Here, the different quantum phases of the system refer to distinct
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
s of the
Hamiltonian matrix In mathematics, a Hamiltonian matrix is a -by- matrix such that is symmetric, where is the skew-symmetric matrix :J = \begin 0_n & I_n \\ -I_n & 0_n \\ \end and is the -by- identity matrix. In other words, is Hamiltonian if and only if ...
. Understanding the behavior of quantum phase transition is important in the difficult tasks of explaining the properties of rare-earth magnetic insulators, high-temperature superconductors, and other substances. Two classes of phase transitions occur: ''first-order transitions'' and ''second-order'' or ''continuous transitions''. For the latter, the two phases involved do not co-exist at the transition temperature, also called the critical point. Near the critical point, systems undergo critical behavior, wherein several of their properties such as
correlation length A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables rep ...
,
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
, and
magnetic susceptibility In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...
diverge exponentially. These critical phenomena present serious challenges to physicists because normal
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena an ...
laws are no longer valid in the region, and novel ideas and methods must be invented to find the new laws that can describe the system. The simplest theory that can describe continuous phase transitions is the
Ginzburg–Landau theory In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
, which works in the so-called
mean-field approximation In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random ( stochastic) models by studying a simpler model that approximates the original by averaging over degrees o ...
. However, it can only roughly explain continuous phase transition for ferroelectrics and type I superconductors which involves long range microscopic interactions. For other types of systems that involves short range interactions near the critical point, a better theory is needed. Near the critical point, the fluctuations happen over broad range of size scales while the feature of the whole system is scale invariant.
Renormalization group In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the ...
methods successively average out the shortest wavelength fluctuations in stages while retaining their effects into the next stage. Thus, the changes of a physical system as viewed at different size scales can be investigated systematically. The methods, together with powerful computer simulation, contribute greatly to the explanation of the critical phenomena associated with continuous phase transition.


Experimental

Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of electric and
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s, measuring
response function In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of sy ...
s, transport properties and
thermometry Temperature measurement (also known as thermometry) describes the process of measuring a current local temperature for immediate or later evaluation. Datasets consisting of repeated standardized measurements can be used to assess temperature tren ...
. Commonly used experimental methods include
spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
, with probes such as
X-rays An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 Picometre, picometers to 10 Nanometre, nanometers, corresponding to frequency, ...
,
infrared light Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
and
inelastic neutron scattering Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. Th ...
; study of thermal response, such as
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
and measuring transport via thermal and heat
conduction Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble, such as an orchestra. * Conductor (album), ''Conductor'' (album), an album by indie rock band The Comas * Conduction, a type of structured f ...
.


Scattering

Several condensed matter experiments involve scattering of an experimental probe, such as
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10  nanometers, corresponding to frequencies in the range 30&nb ...
, optical
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s,
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s, etc., on constituents of a material. The choice of scattering probe depends on the observation energy scale of interest.
Visible light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
has energy on the scale of 1
electron volt In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. ...
(eV) and is used as a scattering probe to measure variations in material properties such as
dielectric constant The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
and
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
. X-rays have energies of the order of 10
keV Kev can refer to: Given name * Kev Adams, French comedian, actor, screenwriter and film producer born Kevin Smadja in 1991 * Kevin Kev Carmody (born 1946), Indigenous Australian singer-songwriter * Kev Coghlan (born 1988), Scottish Grand Prix motor ...
and hence are able to probe atomic length scales, and are used to measure variations in electron charge density.
Neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s can also probe atomic length scales and are used to study scattering off nuclei and electron
spins The spins (as in having "the spins")Diane Marie Leiva. ''The Florida State University College of Education''Women's Voices on College Drinking: The First-Year College Experience"/ref> is an adverse reaction of intoxication that causes a state of v ...
and magnetization (as neutrons have spin but no charge). Coulomb and
Mott scattering Mott scattering in physics, also referred to as spin-coupling inelastic Rutherford scattering, Coulomb scattering, is the separation of the two spin states of an electron beam by scattering the beam off the Coulomb field of heavy atoms. It is named ...
measurements can be made by using electron beams as scattering probes. Similarly,
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collides ...
annihilation can be used as an indirect measurement of local electron density.
Laser spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
is an excellent tool for studying the microscopic properties of a medium, for example, to study
forbidden transition In spectroscopy, a forbidden mechanism (forbidden transition or forbidden line) is a spectral line associated with absorption or emission of photons by atomic nuclei, atoms, or molecules which undergo a transition that is not allowed by a particul ...
s in media with nonlinear optical spectroscopy.


External magnetic fields

In experimental condensed matter physics, external
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s act as
thermodynamic variable In thermodynamics, a thermodynamic state of a system is its condition at a specific time; that is, fully identified by values of a suitable set of parameters known as state variables, state parameters or thermodynamic variables. Once such a set o ...
s that control the state, phase transitions and properties of material systems.
Nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
(NMR) is a method by which external magnetic fields are used to find resonance modes of individual electrons, thus giving information about the atomic, molecular, and bond structure of their neighborhood. NMR experiments can be made in magnetic fields with strengths up to 60 tesla. Higher magnetic fields can improve the quality of NMR measurement data.
Quantum oscillations In condensed matter physics, quantum oscillations describes a series of related experimental techniques used to map the Fermi surface of a metal in the presence of a strong magnetic field. These techniques are based on the principle of Landau qua ...
is another experimental method where high magnetic fields are used to study material properties such as the geometry of the
Fermi surface In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the cryst ...
. High magnetic fields will be useful in experimentally testing of the various theoretical predictions such as the quantized
magnetoelectric effect In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric ...
, image
magnetic monopole In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magneti ...
, and the half-integer
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exh ...
.


Nuclear spectroscopy

The
local structure The local structure is a term in nuclear spectroscopy that refers to the structure of the nearest neighbours around an atom in crystals and molecules. E.g. in crystals the atoms order in a regular fashion on wide ranges to form even gigantic highl ...
, the structure of the nearest neighbour atoms, of condensed matter can be investigated with methods of
nuclear spectroscopy Nuclear spectroscopy is a superordinate concept of methods that uses properties of a nucleus to probe material properties. By emission or absorption of radiation from the nucleus information of the local structure is obtained, as an interaction of ...
, which are very sensitive to small changes. Using specific and radioactive nuclei, the nucleus becomes the probe that interacts with its surrounding electric and magnetic fields (
hyperfine interactions In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucl ...
). The methods are suitable to study defects, diffusion, phase change, magnetism. Common methods are e.g.
NMR Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
,
Mössbauer spectroscopy Mössbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. This effect, discovered by Rudolf Mössbauer (sometimes written "Moessbauer", German: "Mößbauer") in 1958, consists of the nearly recoil-free emission and abso ...
, or
perturbed angular correlation The perturbed γ-γ angular correlation, PAC for short or PAC-Spectroscopy, is a method of nuclear solid-state physics with which magnetic and electric fields in crystal structures can be measured. In doing so, electrical field gradients and the L ...
(PAC). Especially PAC is ideal for the study of phase changes at extreme temperature above 2000 °C due to no temperature dependence of the method.


Cold atomic gases

Ultracold atom Ultracold atoms are atoms that are maintained at temperatures close to 0 kelvin (absolute zero), typically below several tens of microkelvin (µK). At these temperatures the atom's quantum-mechanical properties become important. To reach such low ...
trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in
atomic, molecular, and optical physics Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO theory in ...
. The method involves using optical lasers to form an
interference pattern In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
, which acts as a ''lattice'', in which ions or atoms can be placed at very low temperatures. Cold atoms in optical lattices are used as ''quantum simulators'', that is, they act as controllable systems that can model behavior of more complicated systems, such as frustrated magnets. In particular, they are used to engineer one-, two- and three-dimensional lattices for a
Hubbard model The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each el ...
with pre-specified parameters, and to study phase transitions for
antiferromagnetic In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...
and
spin liquid In condensed matter physics, a quantum spin liquid is a phase of matter that can be formed by interacting quantum spins in certain magnetic materials. Quantum spin liquids (QSL) are generally characterized by their long-range quantum entangleme ...
ordering. In 1995, a gas of
rubidium Rubidium is the chemical element with the symbol Rb and atomic number 37. It is a very soft, whitish-grey solid in the alkali metal group, similar to potassium and caesium. Rubidium is the first alkali metal in the group to have a density higher ...
atoms cooled down to a temperature of 170 nK was used to experimentally realize the
Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67&n ...
, a novel state of matter originally predicted by
S. N. Bose Satyendra Nath Bose (; 1 January 1894 – 4 February 1974) was a Bengali mathematician and physicist specializing in theoretical physics. He is best known for his work on quantum mechanics in the early 1920s, in developing the foundation for ...
and
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
, wherein a large number of atoms occupy one
quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
.


Applications

Research in condensed matter physics has given rise to several device applications, such as the development of the
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
,
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
technology, and several phenomena studied in the context of
nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal o ...
. Methods such as scanning-tunneling microscopy can be used to control processes at the
nanometer 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
scale, and have given rise to the study of nanofabrication. Such molecular machines were developed for example by Nobel laurate in chemistry
Ben Feringa Bernard Lucas Feringa (, born 18 May 1951) is a Dutch synthetic organic chemist, specializing in molecular nanotechnology and homogeneous catalysis. He is the Jacobus van 't Hoff Distinguished Professor of Molecular Sciences, at the Stratingh ...
. He and his team developed multiple molecular machines such as
molecular car The nanocar is a molecule designed in 2005 at Rice University by a group headed by Professor James Tour. Despite the name, the original nanocar does not contain a molecular motor, hence, it is not really a car. Rather, it was designed to answer th ...
, molecular windmill and many more. In
quantum computation Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
, information is represented by quantum bits, or
qubit In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
s. The qubits may
decohere Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave ...
quickly before useful computation is completed. This serious problem must be solved before quantum computing may be realized. To solve this problem, several promising approaches are proposed in condensed matter physics, including
Josephson junction In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mech ...
qubits,
spintronic Spintronics (a portmanteau meaning spin transport electronics), also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-sta ...
qubits using the
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
orientation of magnetic materials, or the topological non-Abelian
anyon In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchangi ...
s from
fractional quantum Hall effect The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which elec ...
states. Condensed matter physics also has important uses for
biophysics Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. ...
, for example, the experimental method of
magnetic resonance imaging Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
, which is widely used in medical diagnosis.


See also

* * * * * * * * * *


Notes


References


Further reading

* Anderson, Philip W. (2018-03-09). ''Basic Notions Of Condensed Matter Physics''. CRC Press. . *Girvin, Steven M.; Yang, Kun (2019-02-28). ''Modern Condensed Matter Physics''. Cambridge University Press. . *Coleman, Piers (2015). "Introduction to Many-Body Physics". ''Cambridge Core''. Retrieved 2020-04-18. *P. M. Chaikin and T. C. Lubensky (2000). ''Principles of Condensed Matter Physics'', Cambridge University Press; 1st edition, * * * Alexander Altland and Ben Simons (2006). ''Condensed Matter Field Theory'', Cambridge University Press, . * Michael P. Marder (2010). ''Condensed Matter Physics, second edition'', John Wiley and Sons, . *Lillian Hoddeson, Ernest Braun, Jürgen Teichmann and Spencer Weart, eds. (1992). ''Out of the Crystal Maze: Chapters from the History of Solid State Physics'', Oxford University Press, .


External links

* {{DEFAULTSORT:Condensed Matter Physics Materials science