Relaxation Operator For Quasiparticles In A Solid

Popular models of the phenomenological relaxation operators that are widely used in the master equation formalism for open condensed-matter systems have significant flaws ranging from limited applicability to violation of fundamental physical principles. We propose a relatively simple universal model of the relaxation operator which is free from these flaws, has a correct static limit, has a correct direct-current limit in a uniform electric field, includes both interband and intraband transitions, and is valid for an arbitrary dispersion of quasiparticles in a solid. We use the proposed operator to generalize the Lindhard formula and derive explicit expressions for the relaxation operator for Dirac materials with an unconventional energy spectrum of quasiparticles, such as graphene and Weyl semimetals. We compare the linear susceptibility spectra for graphene obtained with different relaxation models and show that the proposed relaxation operator leads to physically meaningful behavior of the susceptibility at low frequencies, whereas the existing models become completely invalid.