Spin Hall insulators beyond the Helical Luttinger model

Abstract

We consider the interacting, spin conserving, extended Kane-Mele-Hubbard model, and we rigorously establish the exact quantization of the edge spin conductance and the validity of the Helical Luttinger liquid relations for Drude weights and susceptibilities. Our analysis fully takes into account lattice effects, typically neglected in the Helical Luttinger model approximation, which play an essential role for universality. The analysis is based on exact renormalization group methods and on a combination of lattice and emergent Ward identities, which allow to relate the emergent chiral anomaly with the finite renormalizations due to lattice corrections.

arXiv commentExtended version of the original submission. Figure added, minor corrections. 10 pages, 2 figures. Accepted for publication on Phys. Rev. B

References in corpus (40)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Quantum Spin Hall Effect
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• 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
• Imaging currents in HgTe quantum wells in the quantum spin Hall regime
• Bulk-edge correspondence for two-dimensional topological insulators
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Helical edge resistance introduced by charge puddles
• Correlation effects in two-dimensional topological insulators
• Inelastic electron backscattering in a generic helical edge channel
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Phonon induced backscattering in helical edge states
• Simultaneous quantization of edge and bulk Hall conductivity
• Conductivity of a generic helical liquid
• Localization at the Edge of 2D Topological Insulator by Kondo Impurities with Random Anisotropies
• Equality of bulk and edge Hall conductance revisited
• Topological invariants of edge states for periodic two-dimensional models
• Absence of interaction corrections in graphene conductivity
• Universality of the Hall conductivity in interacting electron systems
• Topological edge states and quantum Hall effect in the Haldane model
• Universality of conductivity in interacting graphene
• Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges
• Non perturbative Adler-Bardeen Theorem
• Universal Relations for Non Solvable Statistical Models
• Helical Quantum Edge Gears in 2D Topological Insulators
• Extended scaling relations for planar lattice models
• Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid
• Topological phase transitions and universality in the Haldane-Hubbard model
• Universality of one-dimensional Fermi systems, I. Response functions and critical exponents
• Universality of one-dimensional Fermi systems, II. The Luttinger liquid structure
• Charge and spin density in the helical Luttinger liquid

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• Correlation Energy of a Weakly Interacting Fermi Gas
• A new approach to transport coefficients in the quantum spin Hall effect
• Quantization of the interacting Hall conductivity in the critical regime
• Universal edge transport in interacting Hall systems
• Multi-Channel Luttinger Liquids at the Edge of Quantum Hall Systems
• Adiabatic Evolution of Low-Temperature Many-Body Systems
• Order, disorder and phase transitions in quantum many body systems
• Anomaly non-renormalization in interacting Weyl semimetals
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure