Quantum interference and spin-charge separation in a disordered Luttinger liquid

A. G. Yashenkin, I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov
Phys. Rev. B 78, 205407 – Published 7 November 2008

Abstract

We study the influence of spin on the quantum interference of interacting electrons in a single-channel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional-bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful LL on an equal footing. We analyze the effect of spin-charge separation at finite temperature both on the spectral properties of single-particle fermionic excitations and on the conductivity of a disordered quantum wire. We demonstrate that the notion of weak localization, related to the interference of multiple-scattered electron waves and their decoherence due to electron-electron scattering, remains applicable to the spin-charge separated system. The relevant dephasing length, governed by the interplay of inelastic electron-electron interactions and spin-charge separation, is found to be parametrically shorter than in a spinless LL. We calculate both the quantum (weak localization) and classical (memory effect) corrections to the conductivity of a disordered spinful LL. The classical correction is shown to dominate in the limit of high temperature.

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  • Received 8 August 2008

DOI:https://doi.org/10.1103/PhysRevB.78.205407

©2008 American Physical Society

Authors & Affiliations

A. G. Yashenkin1,2, I. V. Gornyi1,3, A. D. Mirlin1,2,4, and D. G. Polyakov1

  • 1Institut für Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany
  • 2Theory Division, Petersburg Nuclear Physics Institute, Gatchina, 188300 St. Petersburg, Russia
  • 3A.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
  • 4Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany

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Vol. 78, Iss. 20 — 15 November 2008

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