Condensed matter physics
Condensed matter physics is a branch of physics that deals with the
physical properties of condensed phases of matter, where particles
adhere to each other. Condensed matter physicists seek to understand
the behavior of these phases by using physical laws. In particular,
they include the laws of quantum mechanics, electromagnetism and
The most familiar condensed phases are solids and liquids while more
exotic condensed phases include the superconducting phase exhibited by
certain materials at low temperature, the ferromagnetic and
antiferromagnetic phases of spins on crystal lattices of atoms, and
Bose–Einstein condensate found in ultracold atomic systems. The
study of condensed matter physics involves measuring various material
properties via experimental probes along with using methods of
theoretical physics to develop mathematical models that help in
understanding physical behavior.
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 field overlaps with chemistry, materials science, and
nanotechnology, and relates closely to atomic physics and biophysics.
The theoretical physics of condensed matter shares important concepts
and methods with that of particle physics and nuclear physics.
A variety of topics in physics such as crystallography, metallurgy,
elasticity, magnetism, etc., were treated as distinct areas until the
1940s, when they were grouped together as solid state physics. Around
the 1960s, the study of physical properties of liquids was added to
this list, forming the basis for the new, related specialty of
condensed matter physics. According to physicist Philip Warren
Anderson, the term was coined by him and Volker Heine, when they
changed the name of their group at the Cavendish Laboratories,
Solid state theory to Theory of Condensed
1967, as they felt it did not exclude their interests in the study
of liquids, nuclear matter, and so on. Although Anderson and Heine
helped popularize the name "condensed matter", it had been present in
Europe for some years, most prominently in the form of a journal
published in English, French, and German by Springer-Verlag titled
Physics of Condensed Matter, which was launched in 1963. The
funding environment and Cold War politics of the 1960s and 1970s were
also factors that lead some physicists to prefer the name "condensed
matter physics", which emphasized the commonality of scientific
problems encountered by physicists working on solids, liquids,
plasmas, and other complex matter, over "solid state physics", which
was often associated with the industrial applications of metals and
semiconductors. The Bell Telephone Laboratories was one of the
first institutes to conduct a research program in condensed matter
References to "condensed" state can be traced to earlier sources. For
example, in the introduction to his 1947 book Kinetic Theory of
Yakov Frenkel 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
1.1 Classical physics
1.2 Advent of quantum mechanics
1.3 Modern many-body physics
2.2 Electronic theory of solids
2.3 Symmetry breaking
2.4 Phase transition
3.2 External magnetic fields
3.3 Cold atomic gases
5 See also
8 Further reading
Heike Kamerlingh Onnes
Heike Kamerlingh Onnes and
Johannes van der Waals
Johannes van der Waals with the helium
One of the first studies of condensed states of matter was by English
chemist Humphry Davy, in the first decades of the nineteenth century.
Davy observed that of the forty chemical elements known at the time,
twenty-six had metallic properties such as lustre, ductility and high
electrical and thermal conductivity. This indicated that the atoms
in John Dalton's atomic theory 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 and hydrogen could be
liquefied under the right conditions and would then behave as
In 1823, Michael Faraday, then an assistant in Davy's lab,
successfully liquefied chlorine and went on to liquefy all known
gaseous elements, except for nitrogen, hydrogen, and oxygen.
Shortly after, in 1869, Irish chemist Thomas Andrews studied the phase
transition 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 physicist Johannes van der
Waals supplied the theoretical framework which allowed the prediction
of critical behavior based on measurements at much higher
temperatures.:35–38 By 1908,
James Dewar and Heike Kamerlingh
Onnes were successfully able to liquefy hydrogen and then newly
discovered helium, respectively.
Paul Drude in 1900 proposed the first theoretical model for a
classical electron 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.:27–29 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 and magnetic properties of metals,
and the temperature dependence of resistivity at low
In 1911, three years after helium was first liquefied, Onnes working
at University of
Leiden discovered superconductivity in mercury, 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, 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
Advent of quantum mechanics
Drude's classical model was augmented by Wolfgang Pauli, Arnold
Felix Bloch and other physicists. Pauli realized that the
free electrons in metal must obey the Fermi–Dirac statistics. Using
this idea, he developed the theory of paramagnetism in 1926. Shortly
after, Sommerfeld incorporated the
Fermi–Dirac statistics into the
free electron model and made it better able to explain the heat
capacity. Two years later, Bloch used quantum mechanics to describe
the motion of a quantum electron in a periodic lattice.:366–368
The mathematics of crystal structures developed by Auguste Bravais,
Yevgraf Fyodorov and others was used to classify crystals by their
symmetry group, and tables of crystal structures were the basis for
the series International Tables of Crystallography, first published in
Band structure calculations was first used in 1930 to
predict the properties of new materials, and in 1947 John Bardeen,
Walter Brattain and
William Shockley developed the first
semiconductor-based transistor, heralding a revolution in
A replica of the first point-contact transistor in Bell labs
Edwin Herbert Hall
Edwin Herbert Hall working at the Johns Hopkins University
discovered a voltage developing 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, but it
was not properly explained at the time, since the electron was
experimentally discovered 18 years later. After the advent of quantum
Lev Landau in 1930 developed the theory of Landau
quantization and laid the foundation for the theoretical explanation
for the quantum
Hall effect discovered half a century
Magnetism as a property of matter has been known in China since 4000
BC.:1–2 However, the first modern studies of magnetism only
started with the development of electrodynamics by Faraday, Maxwell
and others in the nineteenth century, which included classifying
materials as ferromagnetic, paramagnetic and diamagnetic based on
their response to magnetization.
Pierre Curie studied the
dependence of magnetization on temperature and discovered the Curie
point phase transition in ferromagnetic materials. In 1906, Pierre
Weiss introduced the concept of magnetic domains to explain the main
properties of ferromagnets.:9 The first attempt at a microscopic
description of magnetism was by
Wilhelm Lenz and
Ernst Ising through
Ising model that described magnetic materials as consisting of a
periodic lattice of spins that collectively acquired
Ising model was solved exactly to show that
spontaneous magnetization cannot occur in one dimension but is
possible in higher-dimensional lattices. Further research such as by
Bloch on spin waves and
Néel on antiferromagnetism led to developing
new magnetic materials with applications to magnetic storage
Modern many-body physics
A magnet levitating above a high-temperature superconductor. Today
some physicists are working to understand high-temperature
superconductivity using the AdS/CFT correspondence.
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 and the
Kondo effect. After World War II, several ideas from quantum field
theory were applied to condensed matter problems. These included
recognition of collective excitation modes of solids and the important
notion of a quasiparticle. Russian physicist
Lev Landau used the idea
Fermi liquid theory 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
for continuous phase transitions, which described ordered phases as
spontaneous breakdown of symmetry. The theory also introduced the
notion of an order parameter to distinguish between ordered
phases. Eventually in 1965, John Bardeen,
Leon Cooper and John
Schrieffer developed the so-called
BCS theory of superconductivity,
based on the discovery that arbitrarily small attraction between two
electrons of opposite spin mediated by phonons in the lattice can give
rise to a bound state called a Cooper pair.
The quantum Hall effect: Components of the Hall resistivity as a
function of the external magnetic field:fig. 14
The study of phase transition and the critical behavior of
observables, termed critical phenomena, was a major field of interest
in the 1960s. Leo Kadanoff,
Benjamin Widom and Michael Fisher
developed the ideas of critical exponents and widom scaling. These
ideas were unified by
Kenneth G. Wilson in 1972, under the formalism
of the renormalization group in the context of quantum field
Hall effect was discovered by
Klaus von Klitzing
Klaus von Klitzing in 1980
when he observed the Hall conductance to be integer multiples of a
displaystyle 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 proposed a theory explaining the unanticipated precision of
the integral plateau. It also implied that the Hall conductance can be
characterized in terms of a topological invariable called Chern
number.:69, 74 Shortly after, in 1982,
Horst Störmer and
Daniel Tsui observed the fractional quantum
Hall effect where the
conductance was now a rational multiple of a constant. Laughlin, in
1983, realized that this was a consequence of quasiparticle
interaction in the Hall states and formulated a variational method
solution, named the Laughlin wavefunction. The study of
topological properties of the fractional
Hall effect remains an active
field of research.
In 1986, Karl Müller and
Johannes Bednorz discovered the first high
temperature superconductor, a material which was superconducting at
temperatures as high as 50 kelvins. 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 materials continues to be an active research topic.
In 2009, David Field and researchers at
Aarhus University discovered
spontaneous electric fields when creating prosaic films[clarification
needed] of various gases. This has more recently expanded to form the
research area of spontelectrics.
In 2012 several groups released preprints which suggest that samarium
hexaboride has the properties of a topological insulator  in
accord with the earlier theoretical predictions. Since samarium
hexaboride is an established Kondo insulator, i.e. a strongly
correlated electron material, the existence of a topological surface
state in this material would lead to a topological insulator with
strong electronic correlations.
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
Band structure and the density functional theory.
Theoretical models have also been developed to study the physics of
phase transitions, such as the Ginzburg–Landau theory, critical
exponents and the use of mathematical methods of quantum field theory
and the renormalization group. Modern theoretical studies involve the
use of numerical computation of electronic structure and mathematical
tools to understand phenomena such as high-temperature
superconductivity, topological phases, and gauge symmetries.
Main article: Emergence
Theoretical understanding of condensed matter physics is closely
related to the notion of 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 excitations behave like photons and
electrons, thereby describing electromagnetism as an emergent
phenomenon. Emergent properties can also occur at the interface
between materials: one example is the lanthanum aluminate-strontium
titanate interface, where two non-magnetic insulators are joined to
create conductivity, superconductivity, and ferromagnetism.
Electronic theory of solids
Main article: Electronic band structure
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 in 1900 with the Drude
model, which explained electrical and thermal properties by describing
a metal as an ideal gas of then-newly discovered electrons. He was
able to derive the empirical
Wiedemann-Franz law and get results in
close agreement with the experiments.:90–91 This classical model
was then improved by
Arnold Sommerfeld who incorporated the
Fermi–Dirac statistics of electrons and was able to explain the
anomalous behavior of the specific heat of metals in the
Wiedemann–Franz law.:101–103 In 1912, The structure of
crystalline solids was studied by
Max von Laue
Max von Laue and Paul Knipping, when
they observed the
X-ray diffraction pattern of crystals, and concluded
that crystals get their structure from periodic lattices of
atoms.:48 In 1928, Swiss physicist
Felix Bloch provided a wave
function solution to the
Schrödinger equation with a periodic
potential, called the Bloch wave.
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
Vladimir Fock and John Slater developed the so-called
Hartree–Fock wavefunction as an improvement over the Thomas–Fermi
Hartree–Fock method accounted for exchange statistics of
single particle electron wavefunctions. In general, it's very
difficult to solve the Hartree–Fock equation. Only the free electron
gas case can be solved exactly.:330–337 Finally in 1964–65,
Pierre Hohenberg and
Lu Jeu Sham proposed the density
functional theory which gave realistic descriptions for bulk and
surface properties of metals. The density functional theory (DFT) has
been widely used since the 1970s for band structure calculations of
variety of solids.
Main article: Symmetry breaking
Some states of matter exhibit symmetry breaking, where the relevant
laws of physics possess some symmetry that is broken. A common example
is crystalline solids, which break continuous translational symmetry.
Other examples include magnetized ferromagnets, which break rotational
symmetry, and more exotic states such as the ground state of a BCS
superconductor, that breaks
U(1) phase rotational symmetry.
Goldstone's theorem in quantum field theory states that in a system
with broken continuous symmetry, there may exist excitations with
arbitrarily low energy, called the Goldstone bosons. For example, in
crystalline solids, these correspond to phonons, which are quantized
versions of lattice vibrations.
Main article: 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.
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
transitions, the temperature is set to absolute zero, and the
non-thermal control parameter, such as pressure or magnetic field,
causes the phase transitions when order is destroyed by quantum
fluctuations originating from the Heisenberg uncertainty principle.
Here, the different quantum phases of the system refer to distinct
ground states of the Hamiltonian. 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
continuous transitions. For the later, the two phases involved do not
co-exist at the transition temperature, also called critical point.
Near the critical point, systems undergo critical behavior, wherein
several of their properties such as correlation length, specific heat,
and magnetic susceptibility diverge exponentially. These critical
phenomena poses serious challenges to physicists because normal
macroscopic 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
The simplest theory that can describe continuous phase transitions is
the Ginzburg–Landau theory, which works in the so-called mean field
approximation. 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.:8–11
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 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
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 fields, measuring response
functions, transport properties and thermometry. Commonly used
experimental methods include spectroscopy, with probes such as X-rays,
infrared light and inelastic neutron scattering; study of thermal
response, such as specific heat and measuring transport via thermal
and heat conduction.
X-ray diffraction pattern from a protein crystal.
Further information: Scattering
Several condensed matter experiments involve scattering of an
experimental probe, such as X-ray, optical photons, neutrons, etc., on
constituents of a material. The choice of scattering probe depends on
the observation energy scale of interest.
Visible light has energy on
the scale of 1 electron volt (eV) and is used as a scattering probe to
measure variations in material properties such as dielectric constant
and refractive index. X-rays have energies of the order of 10 keV and
hence are able to probe atomic length scales, and are used to measure
variations in electron charge density.:33–34
Neutrons can also probe atomic length scales and are used to study
scattering off nuclei and electron spins and magnetization (as
neutrons have spin but no charge). Coulomb and Mott scattering
measurements can be made by using electron beams as scattering
probes.:33–34:39–43 Similarly, positron annihilation can
be used as an indirect measurement of local electron density.
Laser spectroscopy is an excellent tool for studying the microscopic
properties of a medium, for example, to study forbidden transitions in
media with nonlinear optical spectroscopy. :258–259
External magnetic fields
In experimental condensed matter physics, external magnetic fields act
as thermodynamic variables that control the state, phase transitions
and properties of material systems. Nuclear magnetic resonance
(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.:69:185 Quantum oscillations is another
experimental method where high magnetic fields are used to study
material properties such as the geometry of the Fermi surface.
High magnetic fields will be useful in experimentally testing of the
various theoretical predictions such as the quantized magnetoelectric
effect, image magnetic monopole, and the half-integer quantum Hall
Cold atomic gases
Bose–Einstein condensate observed in a gas of ultracold
rubidium atoms. The blue and white areas represent higher density.
Main article: Optical lattice
Ultracold atom trapping in optical lattices is an experimental tool
commonly used in condensed matter physics, and in atomic, molecular,
and optical physics. The method involves using optical lasers to form
an interference pattern, 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 with pre-specified parameters, and to study phase transitions
for antiferromagnetic and spin liquid ordering.
In 1995, a gas of rubidium atoms cooled down to a temperature of 170
nK was used to experimentally realize the Bose–Einstein condensate,
a novel state of matter originally predicted by
S. N. Bose
S. N. Bose and Albert
Einstein, wherein a large number of atoms occupy one quantum
Computer simulation of nanogears made of fullerene molecules. It is
hoped that advances in nanoscience will lead to machines working on
the molecular scale.
Research in condensed matter physics has given rise to several device
applications, such as the development of the semiconductor
transistor, laser technology, and several phenomena studied in
the context of nanotechnology.:111ff Methods such as
scanning-tunneling microscopy can be used to control processes at the
nanometer scale, and have given rise to the study of
In quantum computation, information is represented by quantum bits, or
qubits. The qubits may decohere 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 qubits, spintronic qubits using the spin
orientation of magnetic materials, or the topological non-Abelian
anyons from fractional quantum
Hall effect states.
Condensed matter physics
Condensed matter physics also has important uses for biophysics, for
example, the experimental method of magnetic resonance imaging, which
is widely used in medical diagnosis.
Green's function (many-body theory)
Comparison of software for molecular mechanics modeling
Symmetry in quantum mechanics
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Condensed matter physics
States of matter
Electronic band structure
Spin gapless semiconductor
Quantum Hall effect
Spin Hall effect
Quantum spin Hall effect
Van der Waals
Branches of physics
Quantum field theory
Physics in life science