Quasiparticle

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In condensed matter physics, 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 behaves as if it contained different weakly interacting particles in vacuum.

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For example, as an electron travels through a semiconductor, its motion is disturbed in a complex way by its interactions with other electrons and with atomic nuclei. The electron behaves as though it has a different effective mass travelling unperturbed in vacuum. Such an electron is called an electron quasiparticle. [1] In another example, the aggregate motion of electrons in the valence band of a semiconductor or a hole band in a metal [2] behave as though the material instead contained positively charged quasiparticles called electron holes . Other quasiparticles or collective excitations include the phonon , a quasiparticle derived from the vibrations of atoms in a solid, and the plasmons , a particle derived from plasma oscillation.

These phenomena are typically called quasiparticles if they are related to fermions, and called collective excitations if they are related to bosons, [1] although the precise distinction is not universally agreed upon. [3] 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 condensed matter physics because it can simplify the many-body problem in quantum mechanics. The theory of quasiparticles was started by the Soviet physicist Lev Landau in the 1930s. [4] [5]

Overview

General introduction

Solids are made of only three kinds of particles: electrons, protons, and neutrons. 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) 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

Any system, no matter how complicated, has a ground state along with an infinite series of higher-energy excited states. Energy levels.svg
Any system, no matter how complicated, has a ground state along with an infinite series of higher-energy excited states.

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 Coulomb's law. In principle, the Schrödinger equation predicts exactly how this system will behave. But the Schrödinger equation in this case is a partial differential equation (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 and various excited states 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, 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 is in the ground state, but if one phonon 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). [6]

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 materials, 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 fermion and a "collective excitation" if it is a boson. [1] However, the precise distinction is not universally agreed upon. [3]

There is a difference in the way that quasiparticles and collective excitations are intuitively envisioned. [3] A quasiparticle is usually thought of as being like a dressed particle: 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 phonon, 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 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. [7] [8]

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.

In the heat capacity example, a crystal can store energy by forming phonons, and/or forming excitons, and/or forming plasmons, 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 liquids, which was originally invented for studying liquid helium-3. For these systems a strong similarity exists between the notion of quasiparticle and dressed particles in quantum field theory. 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 collisions 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 particles. In other words, every type of mean-field kinetic equation, and in fact every mean-field theory, involves a quasiparticle concept.

Examples of quasiparticles and collective excitations

This section contains examples of quasiparticles and collective excitations. The first subsection below contains common ones that occur in a wide variety of materials under ordinary conditions; the second subsection contains examples that arise only in special contexts.

More common examples

More specialized examples

See also

Related Research Articles

<span class="mw-page-title-main">Condensed matter physics</span> Branch of 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 phases that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models and predict the properties of extremely large groups of atoms.

<span class="mw-page-title-main">Elementary particle</span> Subatomic particle having no known substructure

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 consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number: electrons and other leptons, quarks, and the fundamental bosons. Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

<span class="mw-page-title-main">Fermion</span> Type of subatomic particle

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin 1/2, spin 3/2, etc. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.

<span class="mw-page-title-main">Exciton</span> Quasiparticle which is a bound state of an electron and an electron hole

An electron and an electron hole that are attracted to each other by the Coulomb force can form a bound state called an exciton. It is an electrically neutral quasiparticle that exists mainly in condensed matter, including insulators, semiconductors, some metals, but also in certain atoms, molecules and liquids. The exciton is regarded as an elementary excitation that can transport energy without transporting net electric charge.

<span class="mw-page-title-main">Fermi liquid theory</span> Theoretical model in physics

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 behavior of many-body systems of particles in which the interactions between particles may be strong. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas, and why other properties differ.

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 emerge from vacuum at short time and space ranges. The concept of virtual particles arises in the perturbation theory of quantum field theory (QFT) where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.

<span class="mw-page-title-main">Polariton</span> Quasiparticles arising from EM wave coupling

In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also known as the avoided crossing principle. Polaritons describe the crossing of the dispersion of light with any interacting resonance. To this extent polaritons can also be thought of as the new normal modes of a given material or structure arising from the strong coupling of the bare modes, which are the photon and the dipolar oscillation. The polariton is a bosonic quasiparticle, and should not be confused with the polaron, which is an electron plus an attached phonon cloud.

<span class="mw-page-title-main">Spontaneous symmetry breaking</span> Symmetry breaking through the vacuum state

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.

In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical properties intermediate between fermions and bosons. In general, the operation of exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as abelian or non-abelian. Abelian anyons, detected by two experiments in 2020, play a major role in the fractional quantum Hall effect.

In condensed matter physics, a Cooper pair or BCS pair is a pair of electrons bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper.

<span class="mw-page-title-main">Luttinger liquid</span> Theoretical model describing interacting fermions in a one-dimensional conductor

A Luttinger liquid, or Tomonaga–Luttinger liquid, is a theoretical model describing interacting electrons in a one-dimensional conductor. Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension.

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 , where e is the electron charge and h is the Planck constant. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. The 1998 Nobel Prize in Physics was awarded to Robert Laughlin, Horst Störmer, and Daniel Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations" The microscopic origin of the FQHE is a major research topic in condensed matter physics.

In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy, and represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and its environment. In electrostatics, the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero. In a condensed matter context relevant to electrons moving in a material, the self-energy represents the potential felt by the electron due to the surrounding medium's interactions with it. Since electrons repel each other the moving electron polarizes, or causes to displace the electrons in its vicinity and then changes the potential of the moving electron fields. These are examples of self-energy.

In mesoscopic physics, ballistic conduction is the unimpeded flow of charge carriers, or energy-carrying particles, over relatively long distances in a material. In general, the resistivity of a material exists because an electron, while moving inside a medium, is scattered by impurities, defects, thermal fluctuations of ions in a crystalline solid, or, generally, by any freely-moving atom/molecule composing a gas or liquid. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.

In condensed matter physics, spin–charge separation is an unusual behavior of electrons in some materials in which they 'split' into three independent particles, the spinon, the orbiton and the holon. The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can behave as independent quasiparticles.

<span class="mw-page-title-main">Alexander Kuzemsky</span> Russian physicist

Alexander Leonidovich Kuzemsky is a Russian theoretical physicist.

<span class="mw-page-title-main">Boson</span> Type of subatomic particle

In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value. Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spin. Every observed subatomic particle is either a boson or a fermion.

A dislon is a quantized field associated with the quantization of the lattice displacement in crystalline solids. It is a localized collective excitation of a crystal dislocation.

References

  1. 1 2 3 4 5 6 Kaxiras, Efthimios (9 January 2003). Atomic and Electronic Structure of Solids. Cambridge University Press. pp. 65–69. ISBN   978-0-521-52339-4.
  2. ↑ Ashcroft; Mermin (1976). Solid State Physics (1st ed.). Holt, Rinehart, and Winston. pp.  299–302. ISBN   978-0030839931.
  3. 1 2 3 Richard D. Mattuck, A guide to Feynman diagrams in the many-body problem, p. 10. "As we have seen, the quasiparticle consists of the original real, individual particle, plus a cloud of disturbed neighbors. It behaves very much like an individual particle, except that it has an effective mass and a lifetime. But there also exist other kinds of fictitious particles in many-body systems, i.e. 'collective excitations'. These do not center around individual particles, but instead involve collective, wavelike motion of all the particles in the system simultaneously."
  4. ↑ "Ultracold atoms permit direct observation of quasiparticle dynamics". Physics World. 18 March 2021. Retrieved 26 March 2021.
  5. ↑ Kozhevnikov, A. B. (2004). Stalin's great science : the times and adventures of Soviet physicists. London, England: Imperial College Press. ISBN   1-86094-601-1. OCLC   62416599.
  6. ↑ Ohtsu, Motoichi; Kobayashi, Kiyoshi; Kawazoe, Tadashi; Yatsui, Takashi; Naruse, Makoto (2008). Principles of Nanophotonics. CRC Press. p. 205. ISBN   9781584889731.
  7. ↑ Gelfert, Axel (2003). "Manipulative success and the unreal". International Studies in the Philosophy of Science. 17 (3): 245–263. CiteSeerX   10.1.1.405.2111 . doi:10.1080/0269859032000169451. S2CID   18345614.
  8. ↑ B. Falkenburg, Particle Metaphysics (The Frontiers Collection), Berlin, Germany: Springer 2007, esp. pp. 243–246.
  9. ↑ Wilczek, Frank (2021). Fundalmentals : Ten Keys to Reality. New York, New York: Penguin Press. p. 88. ISBN   9780735223790. LCCN   2020020086.
  10. ↑ "Physics Today Article".
  11. ↑ "Cosmos magazine". June 2008. Archived from the original on 9 June 2008.
  12. ↑ Wilcek, Frank (2021). Fundamentals : Ten Keys to Reality. New York, New York: Penguin Press. pp. 89–90. ISBN   9780735223790. LCCN   2020020086.
  13. ↑ "Josephson Junctions". Science and Technology Review. Lawrence Livermore National Laboratory.
  14. ↑ Hoffman, J. E.; McElroy, K.; Lee, D. H.; Lang, K. M.; Eisaki, H.; Uchida, S.; Davis, J. C.; et al. (2002). "Imaging Quasiparticle Interference in Bi2Sr2CaCu2O8+δ". Science. 297 (5584): 1148–1151. arXiv: cond-mat/0209276 . Bibcode:2002Sci...297.1148H. doi:10.1126/science.1072640. PMID   12142440. S2CID   95868563.
  15. ↑ Banerjee, A.; Bridges, C. A.; Yan, J.-Q.; et al. (4 April 2016). "Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet". Nature Materials . 15 (7): 733–740. arXiv: 1504.08037 . Bibcode:2016NatMa..15..733B. doi:10.1038/nmat4604. PMID   27043779. S2CID   3406627.
  16. ↑ Shaginyan, V. R.; et al. (2012). "Identification of Strongly Correlated Spin Liquid in Herbertsmithite". EPL . 97 (5): 56001. arXiv: 1111.0179 . Bibcode:2012EL.....9756001S. doi:10.1209/0295-5075/97/56001. S2CID   119288349.
  17. ↑ Schmidt, Richard; Lemeshko, Mikhail (18 May 2015). "Rotation of Quantum Impurities in the Presence of a Many-Body Environment". Physical Review Letters. 114 (20): 203001. arXiv: 1502.03447 . Bibcode:2015PhRvL.114t3001S. doi:10.1103/PhysRevLett.114.203001. PMID   26047225. S2CID   9111150.
  18. ↑ Lemeshko, Mikhail (27 February 2017). "Quasiparticle Approach to Molecules Interacting with Quantum Solvents". Physical Review Letters. 118 (9): 095301. arXiv: 1610.01604 . Bibcode:2017PhRvL.118i5301L. doi:10.1103/PhysRevLett.118.095301. PMID   28306270. S2CID   5190749.
  19. ↑ "Existence of a new quasiparticle demonstrated". Phys.org. Retrieved 1 March 2017.
  20. ↑ Xu, S. Y.; Alidoust, N.; Chang, G.; et al. (2 June 2017). "Discovery of Lorentz-violating type II Weyl fermions in LaAlGe". Science Advances . 3 (6): e1603266. Bibcode:2017SciA....3E3266X. doi:10.1126/sciadv.1603266. PMC   5457030 . PMID   28630919.
  21. ↑ Li, Mingda; Tsurimaki, Yoichiro; Meng, Qingping; Andrejevic, Nina; Zhu, Yimei; Mahan, Gerald D.; Chen, Gang (2018). "Theory of electron–phonon–dislon interacting system—toward a quantized theory of dislocations". New Journal of Physics. 20 (2): 023010. arXiv: 1708.07143 . Bibcode:2018NJPh...20b3010L. doi:10.1088/1367-2630/aaa383. S2CID   119423231.
  22. ↑ Saeed, Imran; Pak, Hyuk Kyu; Tlusty, Tsvi (26 January 2023). "Quasiparticles, flat bands and the melting of hydrodynamic matter". Nature Physics. 19 (4): 536–544. arXiv: 2203.13615 . Bibcode:2023NatPh..19..536S. doi:10.1038/s41567-022-01893-5. ISSN   1745-2481. S2CID   247749037.

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