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.

15 pages, 8 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
• The Quantum Spin Hall Effect: Theory and Experiment
• 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
• 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
• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator

Cited by in corpus (2)

• Tomonaga Luttinger liquid in the topological edge channel of multilayer FeSe
• Majorana bound states in topological insulators with hidden Dirac points