Interaction-induced backscattering in short quantum wires

M.-T. Rieder, T. Micklitz, A. Levchenko, and K. A. Matveev
Phys. Rev. B 90, 165405 – Published 6 October 2014

Abstract

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

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  • Received 7 July 2014
  • Revised 21 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.165405

©2014 American Physical Society

Authors & Affiliations

M.-T. Rieder1, T. Micklitz1,2, A. Levchenko3,4, and K. A. Matveev5

  • 1Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, 14195 Berlin, Germany
  • 2Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
  • 3Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
  • 4Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
  • 5Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

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Issue

Vol. 90, Iss. 16 — 15 October 2014

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