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Conductivity of a generic helical liquid

Kainaris, Nikolaos, Gornyi, Igor V., Carr, Sam T., Mirlin, Alexander D. (2014) Conductivity of a generic helical liquid. Physical Review B, 90 (7). Article Number 075118. ISSN 2469-9950. E-ISSN 2469-9969. (doi:10.1103/PhysRevB.90.075118) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:60001)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
https://doi.org/10.1103/PhysRevB.90.075118

Abstract

A quantum spin Hall insulator is a two-dimensional state of matter consisting of an insulating bulk and one-dimensional helical edge states. While these edge states are topologically protected against elastic backscattering in the presence of disorder, interaction-induced inelastic terms may yield a finite conductivity. By using a kinetic equation approach, we find the backscattering rate τ−1 and the semiclassical conductivity in the regimes of high (ω≫τ−1) and low (ω≪τ−1) frequency. By comparing the two limits, we find that the parametric dependence of conductivity is described by the Drude formula for the case of a disordered edge. On the other hand, in the clean case where the resistance originates from umklapp interactions, the conductivity takes a non-Drude form with a parametric suppression of scattering in the dc limit as compared to the ac case. This behavior is due to the peculiarity of umklapp scattering processes involving necessarily the state at the “Dirac point.” In order to take into account Luttinger liquid effects, we complement the kinetic equation analysis by treating interactions exactly in bosonization and calculating conductivity using the Kubo formula. In this way, we obtain the frequency and temperature dependence of conductivity over a wide range of parameters. We find the temperature and frequency dependence of the transport scattering time in a disordered system as τ∼[max(ω,T)]−2K−2, for K>2/3 and τ∼[max(ω,T)]−8K+2 for K<2/3.

Item Type: Article
DOI/Identification number: 10.1103/PhysRevB.90.075118
Uncontrolled keywords: Physics of Quantum Materials
Divisions: Divisions > Division of Natural Sciences > Physics and Astronomy
Depositing User: Sam Carr
Date Deposited: 23 Jan 2017 09:57 UTC
Last Modified: 17 Aug 2022 11:01 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/60001 (The current URI for this page, for reference purposes)
Carr, Sam T.: https://orcid.org/0000-0001-9995-4944
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