Thermally activated charge carriers and mid-infrared optical excitations in quarter-filled CDW systems

TL;DR

This paper reexamines the optical properties of quarter-filled CDW systems, revealing direct coupling between phase phonons and electric fields, and clarifies the relationship between charge carriers, activation energy, and optical gaps.

Contribution

It introduces a gauge-invariant approach to connect thermally activated charge carriers with optical excitations in CDW systems, challenging previous infrared selection rule assumptions.

Findings

Phase phonons couple directly to electric fields, proportional to CDW magnitude.

The approach links residual, thermally activated, and bound charge carriers.

The relation between charge carriers, activation energy, and optical gaps is clarified.

Abstract

The optical properties of the quarter-filled single-band CDW systems have been reexamined in the model with the electron-phonon coupling related to the variations of electron site energies. It appears that the indirect, electron-mediated coupling between phase phonons and external electromagnetic fields vanishes for symmetry reasons, at variance with the infrared selection rules used in the generally accepted microscopic theory. It is shown that the phase phonon modes and the electric fields couple directly, with the coupling constant proportional to the magnitude of the charge-density wave. The single-particle contributions to the optical conductivity tensor are determined for the ordered CDW state and the related weakly doped metallic state by means of the Bethe--Salpeter equations for elementary electron-hole excitations. It turns out that this gauge-invariant approach establishes a clear connection between the effective numbers of residual, thermally activated and bound charge carriers. Finally, the relation between these numbers and the activation energy of dc conductivity and the optical CDW gap scale is explained in the way consistent with the conductivity sum rules.