Multiple phonon modes in Feynman path-integral variational polaron mobility

TL;DR

This paper extends the Feynman path-integral variational approach to include multiple phonon modes, improving predictions of polaron mobility and revealing richer frequency and temperature-dependent behavior in polar semiconductors.

Contribution

It introduces a multi-phonon mode extension to the Feynman variational polaron model, enhancing the accuracy of mobility predictions and capturing complex phonon interactions.

Findings

The extended model shows better energy estimates and mobility predictions.

It reveals richer structure in mobility due to multiple phonon modes.

The method aligns well with Monte Carlo simulations.

Abstract

The Feynman path-integral variational approach to the polaron problem\cite{Feynman1955}, along with the associated FHIP linear-response mobility theory\cite{Feynman1962}, provides a computationally amenable method to predict the frequency-resolved temperature-dependent charge-carrier mobility, and other experimental observables in polar semiconductors. We show that the FHIP mobility theory predicts non-Drude transport behaviour, and shows remarkably good agreement with the recent diagrammatic Monte-Carlo mobility simulations of Mishchenko et al.\cite{Mishchenko2019} for the abstract Fr\"ohlich Hamiltonian. We extend this method to multiple phonon modes in the Fr\"ohlich model action. This enables a slightly better variational solution, as inferred from the resulting energy. We carry forward this extra complexity into the mobility theory, where it shows richer structure in the frequency and temperature dependent mobility, due to the different phonon modes activating at different energies. The method provides a computationally efficient and fully quantitative method of predicting polaron mobility and response in real materials.