Fractional topological insulators in three dimensions

TL;DR

This work introduces the concept of fractional topological insulator defined by a fractional axion angle and shows that it can be consistent with time reversal T invariance if ground state degeneracies are present.

Abstract

Topological insulators can be generally defined by a topological field theory with an axion angle theta of 0 or pi. In this work, we introduce the concept of fractional topological insulator defined by a fractional axion angle and show that it can be consistent with time reversal (T) invariance if ground state degeneracies are present. The fractional axion angle can be measured experimentally by the quantized fractional bulk magnetoelectric polarization P_3, and a `halved' fractional quantum Hall effect on the surface with Hall conductance of the form (p/q)(e^2/2h) with p,q odd. In the simplest of these states the electron behaves as a bound state of three fractionally charged `quarks' coupled to a deconfined non-Abelian SU(3) `color' gauge field, where the fractional charge of the quarks changes the quantization condition of P_3 and allows fractional values consistent with T-invariance.

Figures (1)

• Figure 1: a) Quark picture of fractional TI with flavor and color degrees of freedom; b) surface FQHE vs transport measurements [Eq. (\ref{['pq']})]; c) nontrivial vs trivial fractional TI; d) Witten effect as a probe of bulk topology.