Damping effects in doped graphene: The relaxation-time approximation

Abstract

The dynamical conductivity of interacting multiband electronic systems derived in Ref. 1 is shown to be consistent with the general form of the Ward identity. Using the semiphenomenological form of this conductivity formula, we have demonstrated that the relaxation-time approximation can be used to describe the damping effects in weakly interacting multiband systems only if local charge conservation in the system and gauge invariance of the response theory are properly treated. Such a gauge-invariant response theory is illustrated on the common tight-binding model for conduction electrons in hole-doped graphene. The model predicts two distinctly resolved maxima in the energyloss-function spectra. The first one corresponds to the intraband plasmons (usually called the Dirac plasmons). On the other hand, the second maximum (π plasmon structure) is simply a consequence of the van Hove singularity in the single-electron density of states. The dc resistivity and the real part of the dynamical conductivity are found to be well described by the relaxationtime approximation, but only in the parametric space in which the damping is dominated by the direct scattering processes. The ballistic transport and the damping of Dirac plasmons are thus the questions that require abandoning the relaxation-time approximation.

Changing character of electronic transitions in graphene: From single-particle excitations to plasmons

“…As we can see, at these energies the screening factor D(Q,ω) is exactly 1. This means that the mentioned transitions are not screened, i.e., the peaks in S(Q,ω) are pure SP excitations which appear at the same energies as peaks in E 2 (Q,ω) [11,25]. Blue dots in Figs.…”

“…To analyze the electronic excitation spectrum of a 2D material one can also use the dielectric function within the tight-binding approximation (TBA) [25][26][27]. Instead of the KS wave functions and energies, here one uses the states and energies of the TBA Hamiltonian.…”

Intraband memory function and memory-function conductivity formula in doped graphene

“…[5,33]. Therefore, the induced current density can be shown in terms of the current-dipole correlation function π αα (q, ω) in the following way…”

“…In this approach, we consider the Heisenberg equation for the density operator c † Lkσ c L ′ k+qσ [5,33],…”

“…One of the central questions regarding the relaxation processes is to explain temperature and retardation effects in simple physical terms by using simple enough self-consistent kinetic equations. The memory function is the common name for the k-and ω-dependent relaxation function in such selfconsistent kinetic equations [1][2][3][4][5][6]. The relaxation rate is its imaginary part at zero frequency.…”