Transport statistics of interacting double dot systems: Coherent and non-Markovian effects

Gernot Schaller, Gerold Kießlich, and Tobias Brandes
Phys. Rev. B 80, 245107 – Published 9 December 2009

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 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 telegraphlike 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.

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  • Received 25 August 2009

DOI:https://doi.org/10.1103/PhysRevB.80.245107

©2009 American Physical Society

Authors & Affiliations

Gernot Schaller*, Gerold Kießlich, and Tobias Brandes

  • Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany

  • *gernot.schaller@tu-berlin.de
  • gerold.kiesslich@tu-berlin.de

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Vol. 80, Iss. 24 — 15 December 2009

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