Hindered rotators by off-site ions in solids: Optical conductivity by sombrero potentials

TL;DR

This paper investigates how off-site ions in solids, modeled as hindered rotators with sombrero potentials, influence optical conductivity, providing a theoretical framework and specific examples like alkali halides and layered perovskites.

Contribution

It introduces a quantum mechanical model of hindered rotators using Mathieu functions to analyze optical conductivity in solids with off-center ions.

Findings

Eigenvalue solutions for hindered rotators in 2D using Mathieu functions.

Analysis of optical conductivity for off-center ions in specific solid-state systems.

Theoretical framework linking sombrero potentials to optical properties.

Abstract

We consider the optical conductivity of carriers scattered by local sombrero potentials associated with hindered planar rotators in solids. Examples for hindered rotators are provided by off-center substitutional Li ions in colored alkali halides and off-site apical oxygens O(A) in layered perovskites. We obtain off-center displacements by solving for the vibronic mixing of electronic states at the displacing ion site. The eigenvalue equation of a hindered rotator is solved in 2D by Mathieu's periodic functions, as the rotation is quantized in rotational bands. We discuss the optical conductivities pertaining to each of the exemplified cases.