condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and elec ...

, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely related phenomena that arise when a microscopically complicated system such as a

solid Solid is a state of matter where molecules are closely packed and can not slide past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree to which they are resisted dependent upon the ...

behaves as if it contained different weakly interacting

particle In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...

s in

vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...

. For example, as an

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

travels through a

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

, its motion is disturbed in a complex way by its interactions with other electrons and with

atomic nuclei The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. Aft ...

. The electron behaves as though it has a different effective mass travelling unperturbed in vacuum. Such an electron is called an ''electron quasiparticle''. In another example, the aggregate motion of electrons in the valence band of a

or a hole band in a metal behave as though the material instead contained positively charged quasiparticles called ''

electron hole In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle denoting the lack of an electron at a position where one could exist in an atom or crystal structure, atomic lattice. Since in ...

s''. Other quasiparticles or collective excitations include the ''

phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined a ...

'', a quasiparticle derived from the vibrations of atoms in a solid, and the ''

plasmon In physics, a plasmon is a quantum of plasma oscillation. Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. The plasmon can be considered as a quasiparticle since it arises from the quant ...

'', a particle derived from plasma oscillation. These phenomena are typically called ''quasiparticles'' if they are related to

fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...

s, and called ''collective excitations'' if they are related to

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 half odd-intege ...

s, although the precise distinction is not universally agreed upon. Thus, electrons and electron holes (fermions) are typically called ''quasiparticles'', while phonons and plasmons (bosons) are typically called ''collective excitations''. The quasiparticle concept is important in

because it can simplify the many-body problem in

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

. The theory of quasiparticles was started by the Soviet physicist

Lev Landau Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and ma ...

in the 1930s.

Overview

General introduction

Solid Solid is a state of matter where molecules are closely packed and can not slide past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree to which they are resisted dependent upon the ...

s are made of only three kinds of

particles In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...

proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...

s, and

neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...

s. None of these are quasiparticles; instead a quasiparticle is an '' emergent phenomenon'' that occurs inside the solid. Therefore, while it is quite possible to have a single particle (electron, proton, or neutron) floating in space, a quasiparticle can only exist inside interacting many-particle systems such as solids. Motion in a solid is extremely complicated: Each electron and proton is pushed and pulled (by

Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that calculates the amount of force (physics), force between two electric charge, electrically charged particles at rest. This electric for ...

) by all the other electrons and protons in the solid (which may themselves be in motion). It is these strong interactions that make it very difficult to predict and understand the behavior of solids (see many-body problem). On the other hand, the motion of a ''non-interacting'' classical particle is relatively simple; it would move in a straight line at constant velocity. This is the motivation for the concept of quasiparticles: The complicated motion of the ''real'' particles in a solid can be mathematically transformed into the much simpler motion of imagined quasiparticles, which behave more like non-interacting particles. In summary, quasiparticles are a mathematical tool for simplifying the description of solids.

Relation to many-body quantum mechanics

The principal motivation for quasiparticles is that it is almost impossible to ''directly'' describe every particle in a macroscopic system. For example, a barely-visible (0.1mm) grain of sand contains around 10¹⁷ nuclei and 10¹⁸ electrons. Each of these attracts or repels every other by

. In principle, the

Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...

predicts exactly how this system will behave. But the Schrödinger equation in this case is a

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

(PDE) on a 3×10¹⁸-dimensional vector space—one dimension for each coordinate (x, y, z) of each particle. Directly and straightforwardly trying to solve such a PDE is impossible in practice. Solving a PDE on a 2-dimensional space is typically much harder than solving a PDE on a 1-dimensional space (whether analytically or numerically); solving a PDE on a 3-dimensional space is significantly harder still; and thus solving a PDE on a 3×10¹⁸-dimensional space is quite impossible by straightforward methods. One simplifying factor is that the system as a whole, like any quantum system, has a

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 ...

and various

excited state In quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Add ...

s with higher and higher energy above the ground state. In many contexts, only the "low-lying" excited states, with energy reasonably close to the ground state, are relevant. This occurs because of the

Boltzmann distribution In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability tha ...

, which implies that very-high-energy thermal fluctuations are unlikely to occur at any given temperature. Quasiparticles and collective excitations are a type of low-lying excited state. For example, a crystal at

absolute zero Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 ° ...

is in the

, but if one

is added to the crystal (in other words, if the crystal is made to vibrate slightly at a particular frequency) then the crystal is now in a low-lying excited state. The single phonon is called an ''elementary excitation''. More generally, low-lying excited states may contain any number of elementary excitations (for example, many phonons, along with other quasiparticles and collective excitations). When the material is characterized as having "several elementary excitations", this statement presupposes that the different excitations can be combined. In other words, it presupposes that the excitations can coexist simultaneously and independently. This is never ''exactly'' true. For example, a solid with two identical phonons does not have exactly twice the excitation energy of a solid with just one phonon, because the crystal vibration is slightly anharmonic. However, in many materials, the elementary excitations are very ''close'' to being independent. Therefore, as a ''starting point'', they are treated as free, independent entities, and then corrections are included via interactions between the elementary excitations, such as "phonon- phonon scattering". Therefore, using quasiparticles / collective excitations, instead of analyzing 10¹⁸ particles, one needs to deal with only a handful of somewhat-independent elementary excitations. It is, therefore, an effective approach to simplify the many-body problem in quantum mechanics. This approach is not useful for ''all'' systems, however. For example, in

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 fermi ...

s, the elementary excitations are so far from being independent that it is not even useful as a starting point to treat them as independent.

Distinction between quasiparticles and collective excitations

Usually, an elementary excitation is called a "quasiparticle" if it is a

and a "collective excitation" if it is a

. However, the precise distinction is not universally agreed upon. There is a difference in the way that quasiparticles and collective excitations are intuitively envisioned. A quasiparticle is usually thought of as being like a

dressed particle In theoretical physics, the term dressed particle refers to a bare particle together with some excitations of other quantum fields that are physically inseparable from the bare particle. For example, a dressed electron includes the cloud of virt ...

: it is built around a real particle at its "core", but the behavior of the particle is affected by the environment. A standard example is the "electron quasiparticle": an electron in a crystal behaves as if it had an effective mass which differs from its real mass. On the other hand, a collective excitation is usually imagined to be a reflection of the aggregate behavior of the system, with no single real particle at its "core". A standard example is the

, which characterizes the vibrational motion of every atom in the crystal. However, these two visualizations leave some ambiguity. For example, a magnon in a

ferromagnet Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromag ...

can be considered in one of two perfectly equivalent ways: (a) as a mobile defect (a misdirected spin) in a perfect alignment of magnetic moments or (b) as a quantum of a collective spin wave that involves the precession of many spins. In the first case, the magnon is envisioned as a quasiparticle, in the second case, as a collective excitation. However, both (a) and (b) are equivalent and correct descriptions. As this example shows, the intuitive distinction between a quasiparticle and a collective excitation is not particularly important or fundamental. The problems arising from the collective nature of quasiparticles have also been discussed within the philosophy of science, notably in relation to the identity conditions of quasiparticles and whether they should be considered "real" by the standards of, for example,

entity realism Entity realism (also selective realism), sometimes equated with referential realism, is a philosophical position within the debate about scientific realism. It is a variation of realism (independently proposed by Stanford School philosophers Nan ...

Effect on bulk properties

By investigating the properties of individual quasiparticles, it is possible to obtain a great deal of information about low-energy systems, including the flow properties and

heat capacity 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 is a ...

. In the heat capacity example, a crystal can store energy by forming

s, and/or forming

exciton An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb's law, Coulomb force resulting from their opposite charges. It is an electrically neutral quasiparticle regarded as ...

s, and/or forming

s, etc. Each of these is a separate contribution to the overall heat capacity.

History

The idea of quasiparticles originated in Lev Landau's theory of

Fermi liquid Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures. The theory describes the ...

s, which was originally invented for studying liquid

helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron. (In contrast, the most common isotope, helium-4, has two protons and two neutrons.) Helium-3 and hydrogen-1 are the only stable nuclides with ...

. For these systems a strong similarity exists between the notion of quasiparticle and

s in

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

. The dynamics of Landau's theory is defined by a kinetic equation of the mean-field type. A similar equation, the Vlasov equation, is valid for a plasma in the so-called plasma approximation. In the plasma approximation, charged particles are considered to be moving in the electromagnetic field collectively generated by all other particles, and hard

collision In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great for ...

s between the charged particles are neglected. When a kinetic equation of the mean-field type is a valid first-order description of a system, second-order corrections determine the entropy production, and generally take the form of a Boltzmann-type collision term, in which figure only "far collisions" between

virtual particle A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle, which allows the virtual particles to spontaneously emer ...

s. In other words, every type of mean-field kinetic equation, and in fact every mean-field theory, involves a quasiparticle concept.

Common examples

This section contains most common examples of quasiparticles and collective excitations. *In solids, an electron quasiparticle is an

as affected by the other forces and interactions in the solid. The electron quasiparticle has the same charge and spin as a "normal" (

elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a c ...

) electron, and like a normal electron, it is a

. However, its mass can differ substantially from that of a normal electron; see the article effective mass. Its electric field is also modified, as a result of electric field screening. In many other respects, especially in metals under ordinary conditions, these so-called Landau quasiparticles closely resemble familiar electrons; as Crommie's " quantum corral" showed, an STM can image their

interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extra ...

upon scattering. *A

hole A hole is an opening in or through a particular medium, usually a solid Body (physics), body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in m ...

is a quasiparticle consisting of the lack of an electron in a state; it is most commonly used in the context of empty states in the valence band of a

. A hole has the opposite charge of an electron. *A

is a collective excitation associated with the vibration of atoms in a rigid

crystal structure In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat ...

. It is a

quantum In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...

of a

sound wave In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

. *A magnon is a collective excitation associated with the electrons' spin structure in a crystal lattice. It is a quantum of a spin wave. *In materials, a photon quasiparticle is a

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 particles that can ...

as affected by its interactions with the material. In particular, the photon quasiparticle has a modified relation between wavelength and energy (

dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the ...

), as described by the material's index of refraction. It may also be termed a polariton, especially near a resonance of the material. For example, an exciton-polariton is a superposition of an exciton and a photon; a phonon-polariton is a superposition of a phonon and a photon. *A

is a collective excitation, which is the quantum of plasma oscillations (wherein all the electrons simultaneously oscillate with respect to all the ions). *A polaron is a quasiparticle which comes about when an electron interacts with the polarization of its surrounding ions. *An

is an electron and hole bound together.

References

External links

PhysOrg.com
– Scientists find new 'quasiparticles'
Curious 'quasiparticles' baffle physicists
by Jacqui Hayes, Cosmos 6 June 2008. Accessed June 2008 {{Authority control Physical phenomena Condensed matter physics Quantum phases Mesoscopic physics