Iterative summation of path integrals for nonequilibrium molecular quantum transport

TL;DR

This paper introduces a nonperturbative numerical method using iterative path integral summation to analyze nonequilibrium quantum transport in molecular conductors, revealing persistent Franck-Condon blockade effects at low temperatures.

Contribution

It develops an iterative summation of path integrals (ISPI) approach for accurate, nonperturbative analysis of quantum transport in molecular systems.

Findings

Reproduces known analytical results in multiple limits

Studies the crossover regime between limits

Shows Franck-Condon blockade persists at low temperatures

Abstract

We formulate and apply a nonperturbative numerical approach to the nonequilibrium current, $I(V)$, through a voltage-biased molecular conductor. We focus on a single electronic level coupled to an unequilibrated vibration mode (Anderson-Holstein model), which can be mapped to an effective three-state problem. Performing an iterative summation of real-time path integral (ISPI) expressions, we accurately reproduce known analytical results in three different limits. We then study the crossover regime between those limits and show that the Franck-Condon blockade persists in the quantum-coherent low-temperature limit, with a nonequilibrium smearing of step features in the $IV$ curve.