Double path-integral method for obtaining the mobility of the one-dimensional charge transport in molecular chain

TL;DR

This paper develops a path-integral method to analyze charge mobility in one-dimensional molecular chains, revealing how electron-phonon interactions influence transport properties and phase transitions.

Contribution

It introduces a novel analytical approach based on Feynman's path integral to study polaronic effects on charge mobility in molecular chains.

Findings

Mobility decreases exponentially with temperature at low temperatures.

Weak electron-phonon coupling results in large-polaronic behavior.

The results align with known phase transition phenomena in polaron transport.

Abstract

We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in the one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large-polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition \cite{Mish} of transport phenomena related to polaron motion in the molecular chain.