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

TL;DR

This paper develops a comprehensive quantum rate equation framework for analyzing coherent resonant tunneling and shot noise in coupled quantum dots, revealing novel transport phenomena like negative differential conductance and Aharonov-Bohm oscillations.

Contribution

It introduces a generic quantum Langevin equation approach to derive quantum rate equations valid for arbitrary conditions, extending previous models and providing new insights into quantum transport.

Findings

Observation of negative differential conductance in series-CQD due to bias and Coulomb effects.

Detection of Aharonov-Bohm oscillations and flux-controlled transport in parallel CQD.

Validation of classical Schottky noise formula for small quantum devices with internal coupling.

Abstract

We carry out a detailed analysis of coherent resonant tunneling through two coupled quantum dots (CQD) in a parallel arrangement in the weak tunneling limit. We establish a set of quantum rate equations (QREs) 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 formulae. 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 NDC 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 AB oscillations of current, and magnetic-flux-controllable negative differential conductance and a huge Fano factor.