Optical properties of the Q1D multiband models -- the transverse equation of motion approach

TL;DR

This paper uses the transverse equation of motion approach to analyze the optical properties of quasi-one-dimensional multiband models, resolving longstanding issues and aligning theoretical results with experimental data.

Contribution

It introduces an exact summation method for singular terms in optical conductivity calculations and applies it to Q1D two-band models with impurity scattering.

Findings

Total optical conductivity reduces to Boltzmann results at zero frequency.

Impurity scattering treatment matches experimental DC conductivity in CDW states.

Numerical calculations for typical Q1D cases demonstrate the model's applicability.

Abstract

The electrodynamic features of the multiband model are examined using the transverse equation of motion approach in order to give the explanation of several long-standing problems. It turns out that the exact summation of the most singular terms in powers of $1/\omega^{n}$ leads to the total optical conductivity which, in the zero-frequency limit, reduces to the results of the Boltzmann equation, for both the metallic and semiconducting two-band regime. The detailed calculations are carried out for the quasi-one-dimensional (Q1D) two-band model corresponding to imperfect charge-density-wave (CDW) nesting. It is also shown that the present treatment of the impurity scattering processes gives the DC conductivity of the ordered CDW state in agreement with the experimental observation. Finally, the DC and optical conductivity are calculated numerically for a few typical Q1D cases.