Quasiparticle

A quasiparticle is an excitation of an interacting physical system that behaves, within a particular range of energies and timescales, like a particle. Its properties arise from the system as a whole rather than from an isolated elementary constituent. In condensed matter physics, quasiparticles make it possible to describe complicated interacting matter in terms of comparatively simple, often weakly interacting excitations. Examples include electrons modified by their surroundings, quantized lattice vibrations, and hybrid light–matter modes. The quasiparticle description is an effective description of observable physical excitations, not a claim that new elementary particles have been created. (nobelprize.org)

Physical meaning

The microscopic constituents of a solid or liquid interact continuously. Adding an electron, for example, changes the motion and distribution of other particles. The resulting excitation therefore consists not simply of the added electron but of the electron together with the surrounding system’s response. This is often described as a dressed particle: interactions are incorporated into its effective properties, leaving residual interactions between quasiparticles. The microscopic interactions can be strong even when the low-energy quasiparticles are relatively weakly interacting. (nobelprize.org)

A quasiparticle can have a dispersion relation, effective mass, lifetime, and electric charge different from those suggested by a naive picture of the underlying constituents. These properties belong to an excitation in a medium. For example, the mass characterizing the response of a conduction-electron quasiparticle is not simply the electron’s vacuum rest mass. (nature.com)

Two related usages occur. In the narrower Landau sense, a quasiparticle is a long-lived excitation corresponding to a dressed microscopic particle. In broader usage, the term also includes collective modes and hybrid excitations, such as phonons, magnons, and polaritons. These need not correspond to adding one microscopic constituent: a phonon represents a quantum of coordinated atomic vibration. (nobelprize.org)

Dispersion, spectral weight, and lifetime

A quasiparticle’s dispersion relation $E(\mathbf{k})$ specifies its energy as a function of wave vector $\mathbf{k}$. In an interacting electronic system, both this relation and the excitation’s lifetime can be obtained from the many-body Green function and its self-energy, which encodes interaction effects. The real part of the self-energy shifts the excitation energy; the imaginary part describes damping. (doi.org)

Near a well-defined electronic quasiparticle peak, the retarded Green function can be approximated by

Here $E_{\mathbf{k}}$ is the quasiparticle energy, $\gamma_{\mathbf{k}}$ characterizes its linewidth, $Z_{\mathbf{k}}$ is its quasiparticle residue, and $G^R_{\mathrm{inc}}$ represents the incoherent background. The corresponding spectral function has a concentrated peak superimposed on less coherent spectral weight. The residue measures the weight of the coherent excitation in the single-particle response; it is not the quasiparticle’s electric charge or mass. (pmc.ncbi.nlm.nih.gov)

A narrow intrinsic linewidth indicates a long-lived excitation. For a Landau quasiparticle, the lifetime must be long compared with the characteristic timescale associated with its excitation energy. Merely assigning a peak position to a broad spectrum does not establish that a useful particle description exists. Moreover, experimentally measured broadening can include effects other than intrinsic decay, such as averaging over different momenta. (nature.com)

Landau theory and historical development

Lev Landau’s theory of quantum liquids established quasiparticles as a central organizing concept. In his description of normal liquid helium-3, strongly interacting fermions are replaced at low energies by dressed quasiparticles whose mutual interactions are described by a small set of phenomenological parameters. His theory also predicted zero sound, a collective mode that persists in the low-temperature regime where collisions become infrequent; this prediction was subsequently confirmed experimentally. (nobelprize.org)

Landau introduced Fermi-liquid theory in the 1950s, with his paper The Theory of a Fermi Liquid published in 1956. The theory became a framework for understanding normal helium-3 and many metals. Landau received the Nobel Prize in Physics in 1962 for his theories of condensed matter, especially liquid helium; the award was not restricted to quasiparticles alone. (jetp.ras.ru)

In an ordinary Fermi liquid, quasiparticles become increasingly long-lived as their energy approaches the chemical potential and temperature decreases. For a conventional three-dimensional Fermi liquid, the electron–electron contribution to the low-energy scattering rate has the characteristic form

up to a material-dependent coefficient, where $\xi$ is the excitation energy relative to the chemical potential. The rapid decrease of this rate is what allows a particle-like low-energy description despite interactions. (nature.com)

Major examples

Quasiparticles differ in what is excited, how they propagate, and which quantum numbers they carry.

Electronic dressing and phonons illustrate the distinction between particle-derived and collective excitations. Magnons represent the magnetic counterpart of quantized collective waves. Excitons and polaritons show that quasiparticles can also be bound or hybrid objects rather than simply modified electrons. (nobelprize.org)

In superconductors, Bogoliubov quasiparticles should be distinguished from Cooper pairs. The pairs form the paired background state, whereas the quasiparticles are excitations above it. Their electron–hole mixing and characteristic dispersion are central features of BCS theory and have been investigated using photoemission spectroscopy. (cfm.ehu.es)

More unusual quasiparticles occur in the fractional quantum Hall effect. Some carry electric charge equal to a fraction of the elementary charge, such as $e/3$. This fractional charge describes an excitation of a correlated electron system; it does not mean that an isolated electron has been divided into smaller elementary particles. (nobelprize.org)

Observation and applications

Quasiparticles are studied through the response of matter to experimental probes. Angle-resolved photoemission spectroscopy measures electronic excitations with energy and momentum resolution. Quasiparticle dispersions, spectral weights, and linewidths can therefore be investigated through their spectral signatures, although interpreting the measured intensity requires accounting for how the probe couples to the material. (pmc.ncbi.nlm.nih.gov)

The concept connects microscopic interactions to measurable material properties. Electronic quasiparticles help explain low-temperature electrical transport and optical response in metals. Treating lattice vibrations as a gas of phonons provides a powerful account of the heat capacity of solids. Excitons and polaritons are important in semiconductor optical spectra and in research on light emission, optical nonlinearities, and engineered light–matter interactions. (nature.com)

Computational electronic-structure methods also use quasiparticle energies. The GW approximation, for example, estimates interaction-corrected charged excitation energies and is widely used in theoretical photoemission spectroscopy and calculations of electronic excitations in molecules and materials. (arxiv.org)

Limits of the description

A quasiparticle description is valid only within an appropriate regime. An excitation that is sharply defined at low energy may become strongly damped at higher energy or temperature. Strong correlations can redistribute spectral weight, change effective parameters, and ultimately undermine a conventional electron-like quasiparticle picture. Experiments near a metal–insulator transition also show that poor metallic transport need not immediately imply the complete absence of quasiparticles. (doi.org)

Failure of the Landau description does not necessarily mean that all particle-like excitations disappear. In one-dimensional quantum liquids, alternative collective and fractional excitations provide useful descriptions, and the relation between microscopic particles and emergent excitations can differ substantially from that in a conventional metal. Consequently, the existence of quasiparticles must be assessed for a specified excitation and observable, rather than treated as an all-or-nothing property of a material. (arxiv.org)

References

1. David M. Lee — Nobel Lecturenobelprize.org
2. Rise and fall of Landau’s quasiparticles while approaching the Mott transitionnature.com
3. Density-functional Green function theory: dynamical exchange-correlation field in lieu of self-energydoi.org
4. The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopypmc.ncbi.nlm.nih.gov
5. Fermi polarons at finite temperature: Spectral function and rf-spectroscopyarxiv.org
6. The Theory of a Fermi Liquidjetp.ras.ru
7. The Nobel Prize in Physics 1962nobelprize.org
8. Exciton-Photonics: From Fundamental Science to Applicationsarxiv.org
9. BCS-like Bogoliubov Quasiparticles in High-Tc Superconductors Observed by Angle-Resolved Photoemission Spectroscopyarxiv.org