Conductivity of a generic helical liquid

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 ${\tau }^{-1}$ and the semiclassical conductivity in the regimes of high ($\omega \gg {\tau }^{-1}$) and low ($\omega \ll {\tau }^{-1}$) 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 $\tau \sim [\max (\omega ,T){]}^{-2K-2}$, for $K>2/3$ and $\tau \sim [\max (\omega ,T){]}^{-8K+2}$ for $K<2/3$.

28 pages, 6 figures

References in corpus (12)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid
• Electron transport in disordered Luttinger liquid
• Transport of charge-density waves in the presence of disorder: Classical pinning vs quantum localization
• Frequency-Temperature Crossover in the Conductivity of Disordered Luttinger Liquids

Cited by in corpus (21)

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• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Mesoscopic transport in two-dimensional topological insulators
• Polarized heat current generated by quantum pumping in two-dimensional topological insulators
• Current noise from a magnetic moment in a helical edge
• Levitons in helical liquids with Rashba spin-orbit coupling probed by a superconducting contact
• Backscattering in a helical liquid induced by Rashba spin-orbit coupling and electron interactions: locality, symmetry, and cutoff aspects
• Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological vs. quantum spin and anomalous Hall insulators
• Spin Hall insulators beyond the Helical Luttinger model
• Coulomb drag between helical Luttinger liquids
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator
• Finite frequency backscattering current noise at a helical edge
• Conductance oscillations at the interface between a superconductor and the helical edge channel in a narrow HgTe quantum well
• Localized surfaces of three dimensional topological insulators
• Localization of trivial edge states in InAs/GaSb composite quantum wells
• Microwave Photoresistance of a Two-Dimensional Topological Insulator in a HgTe Quantum Well
• Electronic thermal conductivity in 2D topological insulator in a HgTe quantum well
• Marginally localized edges of time-reversal symmetric topological superconductors
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Finite-temperature spectroscopy of dirty helical Luttinger liquids