Edge states for topological insulators in two dimensions and their Luttinger-like liquids

Abstract

Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac hamiltonians on the boundary with symmetry protected zero modes. This holographic characterization of topological insulators is studied in two dimensions. Dirac hamiltonians on the one dimensional edge are classified according to the discrete symmetries of time-reversal, particle-hole, and chirality, extending a previous classification in two dimensions. We find 17 inequivalent classes, of which 11 have protected zero modes. Although bulk topological invariants are thus far known for only 5 of these classes, we conjecture that the additional 6 describe edge states of new classes of topological insulators. The effects of interactions in two dimensions are also studied. We show that all interactions that preserve the symmetries are exactly marginal, i.e. preserve the gaplessness. This leads to a description of the distinct variations of Luttinger liquids that can be realized on the edge.

13 pages with 4 Tables. Version 2: published version. Some clarifying discussions has been added; main results are unchanged

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Cited by in corpus (7)

• Protected boundary states in gapless topological phases
• Quantum transport of disordered Weyl semimetals at the nodal point
• Interaction effect on topological classification of superconductors in two dimensions
• Topological kink states at a tilt boundary in gated multi-layer graphene
• Counter-propagating edge modes and topological phases of a kicked quantum Hall system
• The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime
• Discrete symmetries of low-dimensional Dirac models: A selective review with a focus on condensed-matter realisations