Models of three-dimensional fractional topological insulators

TL;DR

This paper explores theoretical models of three-dimensional fractional topological insulators, focusing on emergent gauge theories that support fractionalized excitations and their phases, advancing understanding of their microscopic descriptions.

Contribution

It demonstrates that both Abelian and non-Abelian gauge theories can model fractional topological insulators with quantized axion angles, identifying conditions for their phases and ground state properties.

Findings

Coulomb and Higgs phases support fractional topological insulators

Ground state degeneracy varies with manifold topology

Boundary effects induce additional topological terms

Abstract

Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle theta of zero or pi. It was recently shown that fractional quantized values of theta are consistent with time-reversal invariance if deconfined, gapped, fractionally charged bulk excitations appear in the low-energy spectrum due to strong correlation effects, leading to the concept of a fractional topological insulator. These fractionally charged excitations are coupled to emergent gauge fields which ensure that the microscopic degrees of freedom, the original electrons, are gauge-invariant objects. A first step towards the construction of microscopic models of fractional topological insulators is to understand the nature of these emergent gauge theories and their corresponding phases. In this work, we show that low-energy effective gauge theories of both Abelian or non-Abelian type are consistent with a fractional quantized axion angle if they admit a Coulomb phase or a Higgs phase with gauge group broken down to a discrete subgroup. The Coulomb phases support gapless but electrically neutral bulk excitations while the Higgs phases are fully gapped. The Higgs and non-Abelian Coulomb phases exhibit multiple ground states on boundaryless spatial 3-manifolds with nontrivial first homology, while the Abelian Coulomb phase has a unique ground state. The ground state degeneracy receives an additional contribution on manifolds with boundary due to the induced boundary Chern-Simons term.