Fractional topological insulators in three dimensions

TL;DR

This paper introduces the concept of fractional topological insulators in three dimensions, characterized by a fractional axion angle, and discusses their experimental signatures and underlying theoretical framework.

Contribution

It defines fractional topological insulators with fractional axion angles, consistent with time-reversal symmetry, and explores their physical properties and theoretical models.

Findings

Fractional axion angles can be measured via quantized bulk polarization.

Surface exhibits a halved fractional quantum Hall effect with specific Hall conductance.

Electron behaves as a bound state of three fractional charges coupled to a non-Abelian gauge field.

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.