Backscattering in a helical liquid induced by Rashba spin-orbit coupling and electron interactions: locality, symmetry, and cutoff aspects

Abstract

The combination of the time-reversal-symmetric single-particle backscattering field (commonly known as Rashba spin-orbit coupling) and non-backscattering electron interactions is generally expected to produce inelastic backscattering in 1D helical electron liquids at the edge of 2D topological insulators, as theoretically predicted in a number of works. An opposite conclusion of absent backscattering was reached in a recent work [H.-Y. Xie et al., Phys. Rev. Lett. 116, 086603 (2016)] for the "local" model of the backscattering field and interactions. Motivated to resolve this potential controversy, in the present work, we study backscattering effects employing fermionic perturbation theory and considering quite general forms of the backscattering field and electron interactions. We discover that backscattering effects are crucially sensitive to the locality properties of the backscattering field and electron interactions, to the symmetry of the latter, as well as to the presence or absence of the cutoff of the electron spectrum. We find that backscattering is indeed absent under the following assumptions: (i) local backscattering field; (ii.a) local or (ii.b) SU(2)-symmetric interactions; (iii) absent cutoff of the edge-state spectrum. However, violation of any of these conditions leads to backscattering. This also reconciles with the results based on the bosonization technique. We calculate the associated backscattering current, establish its low-bias scaling behavior, and predict a crossover between two different scaling regimes. The main implication of our findings is that backscattering of some magnitude is inevitable in a real system, although could be quite suppressed for nearly local backscattering field and interactions.

arXiv comment15 pages, 8 figures

References in corpus (30)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Bosonization and Strongly Correlated Systems
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• The Quantum Spin Hall Effect: Theory and Experiment
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Landauer Conductance of Luttinger Liquids with Leads
• Transport in an inhomogeneous interacting one--dimensional system
• Bosonization for Beginners --- Refermionization for Experts
• Is there a renormalization of the 1D conductance in Luttinger Liquid model?
• Dynamics of Inhomogeneous Tomonaga-Luttinger Liquid Wire
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Helical edge resistance introduced by charge puddles
• Inelastic electron backscattering in a generic helical edge channel
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Phonon induced backscattering in helical edge states
• Resistance of helical edges formed in a semiconductor heterostructure
• Conductivity of a generic helical liquid
• Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid
• Random Rashba spin-orbit coupling at the quantum spin Hall edge
• Magnetic moments in a helical edge can make weak correlations seem strong
• Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid
• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator
• Evidence for broken Galilean invariance at the quantum spin Hall edge

Cited by in corpus (14)

• Interacting topological insulators: a review
• Interacting topological edge channels
• Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators
• Noise-induced backscattering in a quantum-spin-Hall edge
• Helical Liquids in Semiconductors
• Nontrivial interplay of strong disorder and interactions in quantum spin-Hall insulators doped with dilute magnetic impurities
• Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators
• Tomonaga Luttinger liquid in the topological edge channel of multilayer FeSe
• Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples
• Majorana bound states in topological insulators with hidden Dirac points
• Robustness of Helical Edge States Under Edge Reconstruction
• Backscattering off a driven Rashba impurity at the helical edge
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Edge Reconstruction in a Quantum Spin Hall Insulator