Rashba coupling and magnetic order in correlated helical liquids

Abstract

We study strongly correlated helical liquids with and without Rashba coupling using quantum Monte Carlo simulations of the Kane-Mele model with a Hubbard interaction at the edge. Independent of the Rashba coupling, we find that interactions enhance spin correlations and suppress the spectral weight at the Fermi level. For sufficiently strong interactions, a gap can be observed in the single-particle spectral function. However, based on a finite-size scaling analysis and theoretical arguments, we argue that this gap is closed by order parameter fluctuations in the Luttinger liquid phase even at zero temperature, and filled in by thermally induced kinks in the order parameter in the Mott phase at finite temperatures. While the bosonization suggests an umklapp-driven Mott transition only in the presence of Rashba coupling and hence a significant impact of the latter, our numerical results are almost unaffected by Rashba coupling even at low temperatures.

arXiv comment8 pages, 7 figures, final version

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• Interacting topological insulators: a review
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
• Fractional charge oscillations in quantum spin Hall quantum dots
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• Edge instabilities of topological superconductors
• Helical currents in metallic Rashba strips
• Helical Luttinger liquid on the edge of a 2-dimensional topological antiferromagnet
• Many-Body Effects in Topological Kondo Insulators
• The competition between the intrinsic and Rashba spin-orbit coupling and effects of correlations on Rashba SOC-driven transitions in the Kane-Mele model
• Suppressing backscattering of helical edge modes with a spin bath
• Boundary criticality in two-dimensional interacting topological insulators