Conductivity of CuO$_3$-Chains: Disorder versus Electron-Phonon Coupling

TL;DR

This paper investigates the optical conductivity of CuO$_3$-chains, showing how disorder and electron-phonon interactions influence spectral features, with a focus on polaronic effects and charge-density-wave correlations.

Contribution

It introduces a combined model including disorder and electron-phonon coupling to accurately reproduce experimental optical spectra of CuO$_3$-chains.

Findings

Disorder alone requires unrealistic strength for experimental fit.

Electron-phonon coupling explains high-frequency spectral tail.

Charge-density-wave correlations are significant near half filling.

Abstract

The optical conductivity of the CuO$_3$-chains, a subsystem of the 1-2-3 materials, is dominated by a broad peak in the mid-infrared ($\omega \approx 0.2$eV), and a slowly falling high-frequency tail. The 1D $t$-$J$-model is proposed as the relevant low-energy Hamiltonian describing the intrinsic electronic structure of the CuO$_3$-chains. However, due to charge-spin decoupling, this model alone cannot reproduce the observed $\sw$. We consider two additional scattering mechanisms: (i) Disregarding the not so crucial spin degrees of freedom, the inclusion of strong potential disorder yields excellent agreement with experiment, but suffers from the unreasonable value of the disorder strength necessary for the fit. (ii) Moderately strong polaronic electron-phonon coupling to the mode involving Cu(1)-O(4) stretching, can be modeled within a 1D Holstein Hamiltonian of spinless fermions. Using a variational approximation for the phonon Hilbert space, we diagonalize the Hamiltonian exactly on finite lattices. As a result of the experimental hole density $\approx 1/2$, the chains can exhibit strong charge-density-wave (CDW) correlations, driven by phonon-mediated polaron-polaron interactions. In the vicinity of half filling, charge motion is identified as arising from moving domain walls, \ie defects in the CDW. Incorporating the effect of vacancy disorder by choosing open boundary conditions, good agreement with the experimental spectra is found. In particular, a high-frequency tail arises as a consequence of the polaron-polaron interactions.