Electron Transport Beyond Meir–Wingreen: Many-Body Interactions in a Non-Proportional Coupling Regime

Quantum transport provides a powerful probe of the intrinsic response of materials. In non-interacting systems, transmission is obtained using the Büttiker–Landauer approach. However, many-body interactions complicate this picture, since transport must now account for both coherent and incoherent scattering events. Here we apply the non-equilibrium Green's function formalism to show that charge-flux conservation yields a constraint relating the lesser and the anti-Hermitian parts of the retarded interacting self-energy. From this, we derive a general analytic expression for transmission and current, valid for arbitrary interactions and within the non-proportional coupling regime. We then explore the fully incoherent limit and demonstrate that the well established Meir–Wingreen and Beenakker results emerge as limiting cases of our formulation. Finally, we apply our framework to two model systems—(i) a two-level system and (ii) a quantum dot formed by a nanoribbon coupled via van der Waals interactions to two nanotube electrodes—both in the presence of electron–electron interaction. In both cases, interaction effects generate additional contributions and reveal that incoherent transport induced by e-e interaction gives rise to a new rule governing charge flow in both nanoscale and extended systems, with implications directly connected to experimentally observable responses.