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In physics, quasiparticles and collective excitations (which are closely related) are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different 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 another 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 particles are typically called "quasiparticles" if they are related to fermions (like electrons and holes), and called "collective excitations" if they are related to 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.


General introduction

Solids are made of only three kinds of particles: Electrons, protons, and neutrons. Quasiparticles are none of these; instead they are an emergent phenomenon that occurs inside the solid. Therefore, while it is quite possible to have a single particle (electron or proton or neutron) floating in space, a quasiparticle can instead only exist inside the solid.

Motion in a solid is extremely complicated: Each electron and proton gets 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 particle is quite simple: In classical mechanics, it would move in a straight line, and in quantum mechanics, it would move in a superposition of plane waves. This is the motivation for the concept of quasiparticles: The complicated motion of the actual 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. They are not "real" particles inside the solid. Instead, saying "A quasiparticle is present" or "A quasiparticle is moving" is shorthand for saying "A large number of electrons and nuclei are moving in a specific coordinated way."

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 atoms and 1018 electrons. Each of these attracts or repels every other by Coulomb's law. In quantum mechanics, a system is described by a wavefunction, which, if the particles are interacting (as they are in our case), depends on the position of every particle in the system. So, each particle adds three independent variables to the wavefunction, one for each coordinate needed to describe the position of that particle. Because of this, directly approaching the many-body problem of 1018 interacting electrons by straightforwardly trying to solve the appropriate Schrödinger equation is impossible in practice, since it amounts to solving a partial differential equation not just in three dimensions, but in 3x1018 dimensions – one for each component of the position of each particle.




Therefore, using quasiparticles / collective excitations, instead of analyzing 1018 particles, one needs only to deal with only a handful of somewhat-independent elementary excitations. It is therefore a very effective approach to simplify the many-body problem in quantum mechanics. This approach is not useful for all systems however: 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.2

There is a difference in the way that quasiparticles and collective excitations are intuitively envisioned.2 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": A real electron particle, in a crystal, behaves as if it had a different 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.



Effect on bulk properties





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 quasiparticlescitation needed 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 is most commonly used in the context of empty states in the valence band of a semiconductor.1 A hole has the opposite charge of an electron.

Polariton a coupled photon- exciton or optical phonon. Exciton a coupled hole and electron . Plasmariton a coupled optical phonon and dressed photon consisting of a Plasmon and photon

  • A magnon is a collective excitation1 associated with the electrons' spin structure in a crystal lattice. It is a quantum of a spin wave.

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.6 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/7.7 Second, they can be anyons, an exotic type of particle that is neither a fermion nor boson.8
  • Stoner excitations in ferromagnetic metals

See also


  3. ^ Principles of Nanophotonics by Motoichi Ohtsu, p205 [books.google.com/books?id=3za2u8FnCgUC&pg=PA205 google books link]
  4. ^ A. Gelfert, 'Manipulative Success and the Unreal', International Studies in the Philosophy of Science Vol. 17, 2003, 245–263
  6. ^ Physics Today Article
  7. ^ Cosmos magazine June 2008
  8. ^ Nature article
  10. ^ J. E. Hoffman et al.; McElroy, K; Lee, DH; Lang, KM; Eisaki, H; Uchida, S; Davis, JC (2002). "Imaging Quasiparticle Interference in Bi2Sr2CaCu2O8+". Science 297 (5584): 1148–51. arXiv:cond-mat/0209276. Bibcode:2002Sci...297.1148H. doi:10.1126/science.1072640. PMID 12142440. 

Further reading


External links

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