Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport

TL;DR

This paper presents a unified polaron-based master equation approach to quantum transport in disordered systems, bridging coherent band-like and incoherent hopping regimes, and explains experimental observations in organic semiconductors.

Contribution

It introduces a comprehensive polaron model that captures both transport regimes and their crossover, providing new insights into temperature and coupling effects on diffusion.

Findings

Diffusion coefficient shows non-monotonic dependence on temperature and coupling.

In band-like regime, diffusion is proportional to system-phonon coupling and vanishes at zero coupling.

In hopping regime, diffusion scales with phonon bath relaxation time.

Abstract

Quantum transport in disordered systems is studied using a polaron-based master equation. The polaron approach is capable of bridging the results from the coherent band-like transport regime governed by the Redfield equation to incoherent hopping transport in the classical regime. A non-monotonic dependence of the diffusion coefficient is observed both as a function of temperature and system-phonon coupling strength. In the band-like transport regime, the diffusion coefficient is shown to be linearly proportional to the system-phonon coupling strength, and vanishes at zero coupling due to Anderson localization. In the opposite classical hopping regime, we correctly recover that the dynamics are described by the Fermi's Golden Rule (FGR) and establish that the scaling of the diffusion coefficient depends on the phonon bath relaxation time. In both the hopping and band-like transport regimes, it is demonstrated that at low temperature the zero-point fluctuations of the bath lead to non-zero transport rates, and hence a finite diffusion constant. Application to rubrene and other organic semiconductor materials shows a good agreement with experimental mobility data.