Interplay of topology and interactions in quantum Hall topological insulators: U(1) symmetry, tunable Luttinger liquid, and interaction-induced phase transitions

Abstract

We consider a class of {\em quantum Hall topological insulators}: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counter-propagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyse the edge properties using the formalism of the nonlinear $\sigma$-model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.

27 pages, 16 figures

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Cited by in corpus (10)

• Helical quantum Hall phase in graphene on SrTiO${}_3$
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Testing Topological Protection of Edge States in Hexagonal Quantum Spin Hall Candidate Materials
• Metallic Phase and Temperature Dependence of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Spin-Valley Coherent Phases of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Hall and Faraday effects in interacting multi-band systems with arbitrary band topology and spin-orbit coupling
• Collective excitations in chiral Stoner magnets
• Exotic surface states in hybrid structures of topological insulators and Weyl semimetals
• Exciton Condensation in Landau Levels of Quantum Spin Hall Insulators
• Disorder and quantum transport of the helical quantum Hall phase in graphene