The effects of interaction on quantum spin Hall insulators

Abstract

We study the $S_z$-conserving quantum spin Hall insulator in the presence of Hubbard $U$ from a field theory point view. The main findings are the following. (1) For arbitrarily small U the edges possess power-law correlated antiferromagnetic XY local moments. Gapless charge excitations arise from the Goldstone-Wilczek mechanism. (2) The decaying exponent of the XY correlation is $\ge 2$ hence normally space-time vortices should proliferate. (3) For thermodynamic samples, vortex proliferation is prohibited by the conservation of edge charge. (4) For a sample with finite width electron tunneling between opposite edges allows vortex proliferation hence is a strongly relevant perturbation (more relevant than in the non-interacting theory). (5) The phase transition between the antiferromagnetic and the topological insulating phases is triggered by the condensation of magnetic excitons.

4 pages, 4 figures

References in corpus (14)

• Topological Insulators
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• The quantum spin Hall effect and topological insulators
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Interaction effects and quantum phase transitions in topological insulators
• Spontaneous persistent currents in magnetically ordered graphene ribbons
• Magnetic Response in Quantized Spin Hall Phase of Correlated Electrons

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• Dimensional crossover and cold-atom realization of topological Mott insulators
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• Edge stability and edge quantum criticality in 2D interacting topological insulators
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• Nature of continuous phase transitions in interacting topological insulators
• Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature
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• Topological insulator on honeycomb lattices and ribbons without inversion symmetry
• Quantum phase transition and criticality in quasi one-dimensional spinless Dirac fermions
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
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• Valence Bond Phases in $S=1/2$ Kane-Mele-Heisenberg Model
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