Generalized input-output method to quantum transport junctions. I. General formulation
Junjie Liu, Dvira Segal
Abstract
The interaction of electrons with atomic motion critically influences charge transport properties in molecular conducting junctions and quantum dot systems, and it is responsible for a plethora of transport phenomena. Nevertheless, theoretical tools are still limited to treat simple model junctions in specific parameter regimes. In this paper, which forms the first paper of a series, we put forward a generalized input-output method (GIOM) for studying charge transport in molecular junctions accounting for strong electron-vibration interactions and including electronic and phononic environments. The method radically expands the scope of the input-output theory, which was originally put forward to treat quantum optic problems. Based on the GIOM, we derive a Langevin-type equation of motion for system operators, which possess a great generality and accuracy, and permits the derivation of a stationary charge current expression involving only two types of transfer rates. Furthermore, we devise the so-called polaron transport in electronic resonance approximation, which allows us to feasibly simulate electron dynamics in generic tight-binding models with strong electron-vibration interactions.