Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems

TL;DR

This paper introduces a hierarchical quantum master equation approach that provides a numerically exact method for studying nonequilibrium charge transport in nanosystems with strong electronic-vibrational interactions across various regimes.

Contribution

The paper presents a novel HQME method enabling accurate, numerically exact analysis of nonequilibrium transport with strong vibrational coupling, benchmarking other approximate methods.

Findings

Nonequilibrium effects are significant across all regimes.

Inelastic co-tunneling signals show complex behavior in full nonequilibrium.

The HQME approach benchmarks and validates approximate methods.

Abstract

Within the hierarchical quantum master equation (HQME) framework, an approach is presented, which allows a numerically exact description of nonequilibrium charge transport in nanosystems with strong electronic-vibrational coupling. The method is applied to a generic model of vibrationally coupled transport considering a broad spectrum of parameters ranging from the nonadiabatic to the adiabatic regime and including both resonant and off-resonant transport. We show that nonequilibrium effects are important in all these regimes. In particular in the off-resonant transport regime, the inelastic co-tunneling signal is analyzed for a vibrational mode in full nonequilibrium, revealing a complex interplay of different transport processes and deviations from the commonly used $G_0/2$-thumb-rule. In addition, the HQME-approach is used to benchmark approximate master equation and nonequilibrium Green's function methods.