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

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.