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 G0/2-thumb-rule. In addition, the HQME-approach is used to benchmark approximate master equation and nonequilibrium Green's function methods.Nanosystems are often characterized by strong coupling between electronic and vibrational or structural degrees of freedom. Examples include single-molecule junctions, 1-4 nanoelectromechanical systems 5,6 as well as suspended carbon nanotubes.7-9 Strong electronicvibrational coupling manifests itself in vibronic structures in the transport characteristics and may result in a multitude of nonequilibrium phenomena such as currentinduced local heating and cooling, multistability, switching and hysteresis, as well as decoherence, which have been observed experimentally 10-13 and have been the focus of theoretical studies.14-18 While in certain parameter regimes, approximate methods based on, e.g., scattering theory, master equations or nonequilibrium Green's functions (NEGF) have provided profound physical insight into transport mechanisms, 14-25 the theoretical study of strong coupling situations often requires the application of methods that can be systematically converged, i.e. numerically exact methods. Methods developed in this context include path integral approaches, 26-29 the scattering state numerical renormalization group technique 30 and the multilayer multiconfiguration time-dependent Hartree method.
17,31-33In this paper, the hierarchical quantum master equation (HQME) approach is formulated to study nonequilibrium transport in systems with strong electronicvibrational coupling. The HQME approach generalizes perturbative master equation methods by including higher-order contributions as well as non-Markovian memory and allows for the systematic convergence of the results. This approach was originally developed by Tanimura and Kubo in the context of relaxation dynamics.34,35 Yan and coworkers 36,37 as well as Härtle et al. 38,39 have used it to study charge transport in models with electron-electron interaction. An approximate formulation of the HQME method for the treatment of electronic-vibrational coupling was recently proposed.
40Here, we apply the HQME methodology for the first time within a numerically exact formulation to treat nonequilibrium transport in nanosystems with strong electronicvibra...