First-order coherent resonant tunneling through an interacting coupled-quantum-dot interferometer: Generic quantum rate equations and current noise

We carry out a detailed analysis of coherent resonant tunneling through two coupled quantum dots (CQDs) in a parallel arrangement in the weak-tunneling limit. We establish a set of quantum rate equations in terms of the eigenstate representation by means of a generic quantum Langevin equation approach, which is valid for arbitrary bias voltage, temperature, and interdot hopping strength. Based on linear-response theory, we further derive the current and frequency-independent shot noise formulas. Our results reveal that a previously used formula for evaluating Schottky-type noise of a classical single-electron transistor is a direct result of linear-response theory, and it remains applicable for small quantum devices with internal coupling. Our numerical calculations show some interesting transport features (i) for a series CQD: the appearance of a negative differential conductance due to the bias-voltage-induced shifting of bare levels or a finite interdot Coulomb repulsion, and (ii) for a parallel CQD in strong interdot Coulomb repulsion regime: finite-bias-induced Aharonov-Bohm oscillations of current, and magnetic-flux-controllable negative differential conductance and a huge Fano factor.