# Quasiparticles

A quasiparticle is an excitation of a many-particle system that has an energy-momentum relationship ( dispersion relationship ) like a particle . A quasiparticle is usually a collective state of many particles, an elementary excitation or sometimes the bound state of a pair of particles. It is characteristic of quasiparticles, however, that they cannot occur outside of their many-body system.

A well-known example is the defect electrons (“holes”) in a semiconductor , in which the negatively charged valence electrons collectively move in one direction as if a positively charged particle were moving in the opposite direction. Other examples are phonons , magnons , Cooper pairs, and excitons .

The term quasiparticle goes back to Lev Dawidowitsch Landau . He developed a theory about the interaction between conduction electrons in a metal (the theory of Fermi fluid ). The basic idea is to describe the interaction of a conduction electron with its environment by “expanding” the electron by this interaction. He called this extended particle a quasi- electron , since in theory (as a first approximation) it can be treated like a free electron .

## properties

Properties of normal particles such as mass, momentum, energy, wavelength and spin can be assigned to the quasiparticles, such as the effective mass for a conduction electron with interaction with the other electrons (quasi-electron) instead of the actual mass of an electron. To express that these are properties of a quasiparticle, one also speaks of quasi-mass, etc.

Quasiparticles behave like normal particles and can therefore scatter on each other and exchange momentum and energy. They can also be created and destroyed, so for quasiparticles there is no conservation of the number of particles. In other words, the chemical potential of quasiparticles vanishes . ${\ displaystyle \ mu = 0}$ Systems made up of quasiparticles ( photon gas , phonon gas etc.) cannot be described classically . The classic borderline case is impossible in such systems, because because of the fugacity always applies. ${\ displaystyle z = e ^ {\ beta \ mu} \ ll 1}$ ${\ displaystyle \ mu = 0}$ ${\ displaystyle z = 1}$ Quasiparticles that have an integer or half-integer spin behave accordingly like bosons or fermions and accordingly obey the Bose-Einstein or Fermi-Dirac statistics .

Sometimes the quasiparticles have a discrete energy spectrum , and the solid can absorb or emit certain amounts of energy much better than others.

## example

If one regards a crystal as a system of atoms that are bound to one another by elastic forces, the interaction of the atomic cores with one another can be described by an elastic field. The quasiparticles in this field are called phonons . They are plane elastic waves in the solid. The phonons correspond to the eigenstates of a harmonic oscillator in the one-particle case.

If you radiate an electromagnetic wave into a crystal, mainly elastic scattering takes place, the magnitude of the wave vector does not change. However, the wave can also be scattered with the simultaneous generation or destruction of a phonon. The amount of the wave vector of the light changes. This process is known as Raman scattering . From the change in the wave vector one can determine the wave vector of the phonon and from this calculate the binding energies between the atoms of the crystal.

Bosons
Fermions
Further

## literature

• Alexandre M. Zagoskin: Quantum theory of many body systems - techniques and applications . Springer, New York 1998, ISBN 0-387-98384-8 .
• Ch. Kittel: Introduction to Solid State Physics. 10th edition Oldenbourg Verlag, Munich 1993, ISBN 3-486-22716-5
• Ch. Kittel: Quantum Theory of Solids. 2nd Edition. Oldenbourg 1988, ISBN 3-486-20748-2 .
• Ashcroft: Solid State Physics. 2nd Edition. Oldenbourg 2005, ISBN 3-486-57720-4 .
• Kopitzki: Introduction to Solid State Physics. 6th edition. Teubner, 2007, ISBN 978-3-8351-0144-9 .