A quasiparticle is an excitation in a many-body system that behaves like an elementary particle, even though it is not one. Quasiparticles are important in condensed matter physics because they can often be used to model the behavior of materials and phenomena that are too complex to be described by the behavior of their individual atoms or molecules.
In general, quasiparticles arise when a symmetry is broken in a many-body system. For example, in a metal at low temperatures, the electrons fill up all of the available energy levels up to the Fermi level. However, if we heat up the metal, some of the electrons will be excited into higher energy levels. These excited electrons are called “hot” electrons.
The hot electrons interact with each other and with the lattice vibrations (phonons) of the metal. As a result of these interactions, the hot electrons scatter off of each other and slow down. This process is called electron-phonon scattering.
At high temperatures, there are so many hot electrons that they form a plasma—a gas of electrically charged particles. In a plasma, there are no long-range order (no crystal structure) and the collective behavior of the particles must be described using statistical mechanics.
In contrast, at low temperatures most metals have electrical conductivity due to conduction band states which are well defined Bloch states with definite momentum k throughout the Brillouin zone; these states do not interact strongly with each other or with phonons so they do not scatter appreciably. The Fermi level is near the bottom of a conduction band (or one can think about doping semiconductors to create mobile charge carriers). It turns out that as long as there is only weak scattering between these electronic states then they can still be considered non-interacting quasi-particles: this means that their dispersion relation ϵ(k) remains unchanged from its single particle value and we can use Fermi’s golden rule to calculate transition rates between them; furthermore we can use WKB methods or Feynman’s path integral quantization rules for systems with disorder potentials since our Hamiltonian still has eigenstates |kn⟩ which remain valid solutions to Schrödinger’s equation even in presence of such potentials (the corresponding eigenvalues just get shifted by V(r)). Many properties of metals at low temperature T≪EF/kB follow from this simple picture including electrical resistivity ρ=(m*/ne2τ) where τ−1=2πn⟨|Vkk′|2⟩δ(ϵk−ϵk′)/hbar is now just given by impurity scattering since Umklapp processes involving reciprocal lattice vectors become exponentially suppressed at low T; here m*=ℏ2kF/(2m0) where kF=(3π2n)1/3 is now just determined by density n rather than temperature as was previously required when T≫EF/kB and ℏωD where ωD=(4πne2/m*)1/2 now gives an upper bound on optical phonon frequencies since screening reduces their Coulomb interaction strengths at high frequency leaving behind only Debye cutoffs ∼ωDexp[−(ω/ωD)] for Raman intensity vs frequency curves).