Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions

TL;DR

This paper introduces an advanced path-integral simulation method to study nonequilibrium charge transfer and vibrational effects in molecular electronic junctions, revealing detailed transport mechanisms and vibrational instabilities.

Contribution

The authors develop a numerically-exact influence functional path-integral approach capable of handling multiple fermionic and bosonic reservoirs simultaneously, enabling detailed real-time dynamics analysis.

Findings

Excellent agreement with perturbative Master equations at weak coupling

Identification of vibrational instability in current-rectifying junctions

Quantification of coherent versus inelastic transport contributions

Abstract

We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the real-time dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a current-rectifying junction. Our simulations are performed by assuming large molecular vibrational anharmonicity (or low temperature). This allows us to truncate the molecular vibrational mode to include only a two-state system. Exact numerical results are compared to perturbative Master equation calculations demonstrating an excellent agreement in the weak electron-phonon coupling regime. Significant deviations take place only at strong coupling. Our simulations allow us to quantify the contribution of different transport mechanisms, coherent dynamics and inelastic transport, in the overall charge current. This is done by studying two model variants: The first admits inelastic electron transmission only, while the second one allows for both coherent and incoherent pathways.