Variational band theory of vibronic polarons in crystals. III. Numerical calculations

TL;DR

This paper presents numerical solutions to variational equations for vibronic polarons in crystals, revealing their energy-momentum relations and phonon-electron band contributions, advancing understanding of polaron behavior.

Contribution

It introduces a numerical iterative method to solve variational equations for vibronic polarons, providing detailed energy and amplitude mappings in parameter space.

Findings

Energy vs. momentum relations for ground state obtained

Phonon and band Fourier amplitudes mapped in parameter space

Enhanced understanding of vibronic polaron characteristics

Abstract

In the preceding Part II, we derived variational equations for the phonon Fourier amplitudes and for the Fourier amplitudes of the fractional contribution of the electronic bands to the trial variational state. These equations are now solved by means of iterations for each value of the total momentum in order to obtain the energy vs. momentum relation for the ground state. Another result is mapping out the phonon and band Fourier amplitudes in the parameter space of the mixing constant and the electron hopping energy.