Dual Dirac Liquid on the Surface of the Electron Topological Insulator

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 noncompact Uð1Þ 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.

A master bosonization duality

“…These dualities have been the subject of recent attention from a variety of viewpoints. For the special case N = k = N f = 1, these dualities are related to the surface states of time-reversal invariant topological insulators and the fractional quantum Hall effect at half filling [10][11][12][13], lead to a web of dualities [14][15][16][17], and can even be proven on the lattice [18]. They are crucial actors in mapping out the phase diagram of QCD 3 as well as some of its cousins.…”

Three-dimensional topological insulators and bosonization

“…Recently, several authors have suggested that flux attachment also holds for relativistic theories [74][75][76][77][78][79][80]. For example, a map exists between the Dirac fermion and complex scalar theories, both including self-interactions, with the boson coupled to the Chern-Simons field for changing statistics [79,80].…”

Symmetry enriched U(1) quantum spin liquids

“…In the presence of a boundary, this 3 + 1-dimensional "symmetry-enriched" electric-magnetic duality implies interesting and nontrivial dualities between 2 + 1-dimensional quantum field theories [32][33][34][35]. This line of thinking has proven to be very powerful in studying difficult problems in strong correlation physics in two space dimensions.…”