Transport Statistics of Interacting Double Dot Systems: Coherent and Non-Markovian Effects

TL;DR

This paper develops a generalized master equation framework for charge transport in double quantum dot systems, highlighting the importance of coherences and non-Markovian effects on transport statistics and demonstrating improvements over traditional Markovian approximations.

Contribution

It introduces a virtual detector-based coarse-graining method that includes coherences and Lamb shifts, addressing limitations of the Born-Markov-Secular approximation in transport calculations.

Findings

Coherences significantly affect transport cumulants and can prevent unphysical currents.

Interference effects cause strong current suppression and giant Fano factors.

Finite coarse graining times automatically include coherences, improving accuracy.

Abstract

We formalize the derivation of a generalized coarse-graining $n$-resolved master equation by introducing a virtual detector counting the number of transferred charges in single-electron transport. Our approach enables the convenient inclusion of coherences and Lamb shift in counting statistics. As a Markovian example with Lindblad-type density matrices, we consider the Born-Markov-Secular (BMS) approximation which is a special case of the non-Markovian dynamical coarse graining (DCG) approach. For illustration we consider transport through two interacting levels that are either serially or parallelly coupled to two leads held at different chemical potentials. It is shown that the coherences can strongly influence the (frequency-dependent) transport cumulants: In the serial case the neglect of coherences would lead to unphysical currents through disconnected conductors. Interference effects in the parallel setup can cause strong current suppression with giant Fano factors and telegraph-like distribution functions of transferred electrons, which is not found without coherences. We demonstrate that with finite coarse graining times coherences are automatically included and, consequently, the shortcomings of the BMS approximation are resolved.