Predicting polaron mobility in organic semiconductors with the Feynman variational approach

TL;DR

This paper extends Feynman's variational method to model polaron mobility in organic semiconductors, successfully predicting charge-carrier mobility in crystalline Rubrene that aligns with experimental data.

Contribution

It introduces a novel application of the Feynman variational approach to small polarons in lattice systems, enabling direct calculation of mobility using real material data.

Findings

Predicted mobility of 47.72 cm^2 V^{-1} s^{-1} at 300 K for Rubrene.

Demonstrated good agreement with experimental measurements.

Extended the theory to include discrete localization as a function of coupling strength.

Abstract

We extend the Feynman variational method applied to the parabolic-band Fr\"ohlich (continuum) large polaron~\cite{Feynman1955} to a Holstein (lattice) small polaron, with a parabolic-band. This new theory shows a discrete localisation as a function of coupling strength. Having build the theory with the same quasi-particle Lagrangian as the 1955 work, we can directly use the FHIP~\cite{Feynman1962} response theory to calculate DC mobility and complex conductivity. We show that we can take matrix elements from electronic structure calculations on real materials, by modelling charge-carrier mobility in crystalline Rubrene. Good agreement is found to measurement, with a predicted mobility of $\mu = 47.72$~\si{cm^2 V^{-1} s^{-1}} at $300$~\si{K}.