Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling

TL;DR

This paper analytically investigates the optical absorption in half-filled Peierls-distorted chains of non-interacting electrons, deriving explicit formulas and identifying new correction terms affecting the optical response.

Contribution

It provides the first analytical derivation of optical absorption, current operator, and transition matrix elements for Peierls-distorted chains, including new correction terms.

Findings

Identified broad band-to-band transition in the specified frequency range.

Derived explicit expressions for current operator and dipole transition matrix elements.

Revealed the influence of joint density of states and momentum dependence on absorption shape.

Abstract

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tight-binding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width $W$ and dimerization parameter $\delta$. New correction (``$\eta$''-)terms to the current operator are identified. A broad band-to-band transition is found in the frequency range $W\delta < \omega < W$ whose shape is determined by the joint density of states for the upper and lower Peierls subbands and the strong momentum dependence of the transition matrix elements.