Phase diagram of two interacting helical states

Abstract

We consider two coupled time reversal invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges. We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is non-zero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intra-edge interaction is stronger than the inter-edge interaction, the state is characterised as a spin-nematic phase. However in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. Firstly, the gap protects the conducting phase against localization by weak nonmagnetic impurities; and secondly the protected phase hosts localized zero modes on ends of the edge that may be created by sufficiently strong non-magnetic impurities.

9 pages, 6 figures

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Cited by in corpus (14)

• From one-dimensional charge conserving superconductors to the gapless Haldane phase
• Interaction induced topological protection in one-dimensional conductors
• Probing helicity and the topological origins of helicity via non-local Hanbury-Brown and Twiss correlations
• Localization-Driven Correlated States of Two Isolated Interacting Helical Edges
• Transmission through a potential barrier in Luttinger liquids with a topological spin gap
• Stability of a topological insulator: interactions, disorder and parity of Kramers doublets
• Composite helical edges from Abelian fractional topological insulators
• Time-Reversal Soliton Pairs In Even Spin-Chern-Number Higher-Order Topological Insulators
• Interplay between intrinsic and emergent topological protection on interacting helical modes
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Spin-polarized tunneling into helical edge states: asymmetry and conductances
• Marginally localized edges of time-reversal symmetric topological superconductors
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators
• Tunable Competing Electronic Orders in Double Quantum Spin Hall Superlattices