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

TL;DR

This paper develops a comprehensive theoretical framework for calculating the dynamical conductivity tensor in multiband low-dimensional electronic systems with strong interactions, relevant for understanding phase transitions and high-temperature superconductivity.

Contribution

It introduces a systematic method based on semiclassical and Bethe--Salpeter formalisms for analyzing conductivity in complex multiband models with electron-electron interactions.

Findings

Derived diagrammatic expressions for intraband and interband conductivity.

Discussed relations between quantum, transport, and Bethe--Salpeter equations.

Applied formalism to low-dimensional $sp_\alpha$ models with dipole interactions.

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 single-particle 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 $sp_\alpha$ 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-$T_c$ superconductors.