Semiclassical action based on dynamical mean-field theory describing electrons interacting with local lattice fluctuations

TL;DR

This paper develops a semiclassical approach using dynamical mean-field theory to analyze how local lattice fluctuations affect electronic properties, providing new insights into optical conductivity and isotope effects in correlated materials.

Contribution

It introduces an improved semiclassical method combined with dynamical mean-field theory to study electron-lattice interactions, especially in the Holstein model at finite temperatures.

Findings

Spectral weight shifts from high to low frequencies with isotope substitution.

Finite temperature optical conductivity varies with electron-phonon coupling.

Enhanced understanding of the Fermi-liquid to polaron crossover regime.

Abstract

We extend a recently introduced semiclassical approach to calculating the influence of local lattice fluctuations on electronic properties of metals and metallic molecular crystals. The effective action of electrons in degenerate orbital states coupling to Jahn-Teller distortions is derived, employing dynamical mean-field theory and adiabatic expansions. We improve on previous numerical treatments of the semiclassical action and present for the simplifying Holstein model results for the finite temperature optical conductivity at electron-phonon coupling strengths from weak to strong. Significant transfer of spectral weight from high to low frequencies is obtained on isotope substitution in the Fermi-liquid to polaron crossover regime.