Quantum transport equations for low-dimensional multiband electronic systems: I

Abstract

A systematic method of calculating the dynamical conductivity tensor in a general multiband electronic model with strong boson-mediated electron-electron interactions is described. The theory is based on the exact semiclassical expression for the coupling between valence electrons and electromagnetic fields and on the self-consistent Bethe-Salpeter equations for the electron-hole propagators. The general diagrammatic perturbation expressions for the intraband and interband singleparticle conductivity are determined. The relations between the intraband Bethe-Salpeter equation, the quantum transport equation and the ordinary transport equation are briefly discussed within the memory-function approximation. The effects of the Lorentz dipole-dipole interactions on the dynamical conductivity of low-dimensional spα models are described in the same approximation. Such formalism proves useful in studies of different (pseudo)gapped states of quasi-one-dimensional systems with the metal-to-insulator phase transitions and can be easily extended to underdoped two-dimensional high-Tc superconductors.

Damping effects in doped graphene: The relaxation-time approximation

“…[1,[21][22][23][24][25] The result is the expression (B1) in Appendix B. However, for the longitudinal polarization of the fields, the case which is of primary interest here, we can use the gauge E(r, t) = −∂V tot (r, t)/∂r and write the coupling Hamiltonian as…”

“…[16,31] In the diagrammatic language, the memory function M LL (k, q, ω) is nothing but the self-energy of the intraband electron-hole pair in the approximation called the memory-function approximation. [1,14] In the case in which M LL (k, q, ω) is independent of ω, the memory function reduces to the relaxation rate Γ LL α (k) multiplied by i; i.e.,…”

“…[2,12,13] However, if the interactions (bare or renormalized) are retarded, we usually end up analyzing Bethe-Salpeter equations (or the related quantum transport equations) in a way consistent with the Dyson equations for electrons and phonons. [1,14] In graphene, conduction electrons are assumed to be weakly interacting, and, in principle, one can use the approximate solution of the Bethe-Salpeter equations in which the electron-hole self-energy is replaced by the memory function, or even by the frequency-independent relaxation rate. [15] In this paper, the quantum transport equations from Refs.…”

“…The detailed microscopic analysis of the intraband memory function in doped graphene, which is an obvious generalization of the intraband relaxation rate, will be given in the accompanying article. [14] Precisely speaking, this paper is devoted to the electrodynamic properties of weakly interacting multiband electronic systems described by an exactly solvable bare Hamiltonian in the case in which the Lorentz local field corrections are negligible. The Hamiltonian includes also the retarded phonon-mediated electron-electron interactions, the non-retarded long-range and short-range Coulomb interactions, the electron scattering processes from static disorder, and the coupling to external fields.…”

“…We shall label the microscopic longitudinal dielectric function by ε(q, ω), with the macroscopic dielectric function being its value at q ≈ 0. This function is given by [1,16,17] ε(q, ω) ≈ 1 − v(q)χ(q, ω) ≈ ε ∞ (q, ω) − v(q)χ tot (q, ω)…”