Quasiparticle

In physics, quasiparticles (and related collective excitations) are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different (fictitious) weakly interacting particles in free space. For example, as an electron travels through a semiconductor, its motion is disturbed in a complex way by its interactions with all of the other electrons and nuclei; however it approximately behaves like an electron with a different mass traveling unperturbed through free space. This "electron" with a different mass is called an "electron quasiparticle".^[1] In an even more surprising example, the aggregate motion of electrons in the valence band of a semiconductor is the same as if the semiconductor contained instead positively charged quasiparticles called holes. Other quasiparticles or collective excitations include phonons (particles derived from the vibrations of atoms in a solid), plasmons (particles derived from plasma oscillations), and many others.

These fictitious particles are typically called "quasiparticles" if they are fermions (like electrons and holes), and called "collective excitations" if they are bosons (like phonons and plasmons),^[1] although the precise distinction is not universally agreed.^[2]

Quasiparticles are most important in condensed matter physics, as it is one of the few known ways of simplifying the quantum mechanical many-body problem (and as such, it is applicable to any number of other many-body systems).

The opposite of a quasiparticle is an elementary particle.

Description

In the language of many-body quantum mechanics, a quasiparticle is a type of low-lying excited state of the system (a state possessing energy very close to the ground state energy) that is known as an elementary excitation. As a result of this closeness, most of the other low-lying excited states can be viewed as states in which multiple quasiparticles are present, because interactions between quasiparticles become negligible at sufficiently low temperatures. 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.

Most many-body systems possess two types of elementary excitations. The first type, the quasiparticles, correspond to single particles whose motions are modified by interactions with the other particles in the system. The second type of excitation corresponds to a collective motion of the system as a whole. These excitations are called collective modes, and they include phenomena such as zero sound, plasmons, and spin waves.

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 quasi-particle 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 quasi-particle concept.

Note that the use of the term quasiparticle seems to be ambiguous. Some authors use the term in order to distinguish them from real particles, others (including author of the above passage) to describe an excitation similar to a single particle excitation as opposed to a collective excitation. Both definitions mutually exclude each other as with the former definition collective excitations which are no "real" particles are considered to be quasiparticles. 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.^[3][4]

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 in particular, special contexts.

More common examples

• In solids, an electron quasiparticle is an electron 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) electron, and like a normal electron, it is a fermion. However, its mass can differ substantially from that of a normal electron; see the article effective mass.^[1] 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 clearly image their interference upon scattering.
• A hole is a quasiparticle consisting of the lack of an electron in a state; it's most commonly used in the context of empty states in the valence band of a semiconductor.^[1] A hole has the opposite charge of a electron.
• A phonon is a collective excitation associated with the vibration of atoms in a rigid crystal structure. It is a quantum of a sound wave.
• A magnon is a collective excitation^[1] associated with the electrons' spin structure in a crystal lattice. It is a quantum of a spin wave.
• A roton is a collective excitation associated with the rotation of a fluid (often a superfluid). It is a quantum of a vortex.
• In materials, a photon quasiparticle is a photon as affected by its interactions with the material. In particular, the photon quasiparticle has a modified relation between wavelength and energy (dispersion relation), as described by the material's index of refraction. It may also be termed a polariton, especially near a resonance of the material.
• A plasmon 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.

More specialized examples

• Composite fermions arise in a two-dimensional system subject to a large magnetic field, most famously those systems that exhibit the fractional quantum Hall effect.^[5] These quasiparticles are quite unlike normal particles in two ways. First, their charge can be less than the electron charge e. In fact, they have been observed with charges of e/3, e/4, e/5, and e/7.^[6] Second, they can be anyons, an exotic type of particle that is neither a fermion nor boson.^[7]
• Stoner excitations in ferromagnetic metals
• Bogoliubov quasiparticles in superconductors. Superconductivity is carried by Cooper pairs—usually described as pairs of electrons—that move through the crystal lattice without resistance. A broken Cooper pair is called a Bogoliubov quasiparticle.^[8] It differs from the conventional quasiparticle in metal because it combines the properties of a negatively charged electron and a positively charged hole (an electron void). Physical objects like impurity atoms, from which quasiparticles scatter in an ordinary metal, only weakly affect the energy of a Cooper pair in a conventional superconductor. In conventional superconductors, interference between Bogoliubov quasiparticles is tough for an STM to see. Because of their complex global electronic structures, however, high-Tc cuprate superconductors are another matter. Thus Davis and his colleagues were able to resolve distinctive patterns of quasiparticle interference in Bi-2212.^[9]
• A Majorana fermion is a particle which equals its own antiparticle, and can emerge as a quasiparticle in certain superconductors.
• Magnetic monopoles arise in condensed matter systems such as spin ice and carry an effective magnetic charge as well as being endowed with other typical quasiparticle properties such as an effective mass. They may be formed through spin flips in frustrated pyrochlore ferromagnets and interact through a Coulomb potential.

See also

• Mean field theory
• List of quasiparticles
• Fractionalization

References

External links

• PhysOrg.com – Scientists find new 'quasiparticles'
• Curious 'quasiparticles' baffle physicists by Jacqui Hayes, Cosmos 6 June 2008. Accessed June 2008

Further reading

• L. D. Landau, Soviet Phys. JETP. 3:920 (1957)
• L. D. Landau, Soviet Phys. JETP. 5:101 (1957)
• A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (1963, 1975). Prentice-Hall, New Jersey; Dover Publications, New York.
• D. Pines, and P. Nozières, The Theory of Quantum Liquids (1966). W.A. Benjamin, New York. Volume I: Normal Fermi Liquids (1999). Westview Press, Boulder.
• J. W. Negele, and H. Orland, Quantum Many-Particle Systems (1998). Westview Press, Boulder