Model of the electron-phonon interaction and optical conductivity of Ba$_{1-x}$K$_x$BiO$_3$ superconductors

TL;DR

This study models the optical properties of Ba$_{1-x}$K$_x$BiO$_3$ superconductors using a Holstein model, successfully matching experimental data and revealing strong electron-phonon interactions near the phase boundary.

Contribution

It introduces a simple Holstein model with parameters from first principles that accurately describes the optical and electronic properties of Ba$_{1-x}$K$_x$BiO$_3$ compounds.

Findings

The model reproduces the insulating and metallic phases and the transition around x=0.38.

Strong electron-phonon coupling causes spectral weight redistribution and anharmonic phonons.

The metallic phase near the phase boundary is close to the polaronic regime.

Abstract

We investigate the physical properties of the Ba$_{1-x}$K$_x$BiO$_3$ compounds with a focus on the optical properties. Results from the simple Holstein model, describing a single band coupled to an oxygen breathing mode with parameters derived from first principles calculations, are in excellent agreement with a broad range of experimental information. It accounts for an insulating parent compound at $x=0$ %, with a direct- (optical) and an indirect-gap, and a metal insulator transition around $x = 0.38$. Strong electron-phonon coupling leads to spectral weight redistribution over a frequency scale much larger than the characteristic phonon frequency and to strongly anharmonic phonons. We find that the metallic phase in the vicinity of phase boundary is close to the polaronic regime.