Dual Dirac liquid on the surface of the electron topological insulator

TL;DR

The paper introduces the dual Dirac liquid as a gapless, non-Fermi-liquid surface state for the three-dimensional topological insulator, described by odd Dirac cones coupled to a non-compact U(1) gauge field and interpreted as a vortex dual to the conventional Dirac surface state. It shows how this framework unifies access to known interacting surface phases, including a quantum Hall magnet, Fu-Kane superconductor, and T-Pfaffian and composite Dirac liquid states, by tuning mass terms, pairing, or gauge dynamics. A bulk duality perspective based on electric-magnetic duality explains the surface theory, while the physical properties indicate a rich, tunable non-Fermi-liquid behavior with potential relevance to half-filled Landau level physics. The work also discusses subtleties in flavor counting and connects to particle-hole symmetric descriptions of the quantum Hall problem, suggesting broad implications for strongly correlated topological phases.

Abstract

We discuss a non-fermi liquid gapless metallic surface state of the topological band insulator. It has an odd number of gapless Dirac fermions coupled to a non-compact U(1) gauge field. This can be viewed as a vortex dual to the conventional Dirac fermion surface state. This surface duality is a reflection of a bulk dual description discussed recently for the gauged topological insulator. All the other known surface states can be conveniently accessed from the dual Dirac liquid, including the surface quantum hall state, the Fu-Kane superconductor, the gapped symmetric topological order and the "composite Dirac liquid". We also discuss the physical properties of the dual Dirac liquid, and its connection to the half-filled Landau level.