Classification of interacting electronic topological insulators in three dimensions

TL;DR

This paper classifies all possible interacting three-dimensional electronic topological insulators, revealing six new phases without non-interacting counterparts, and establishes a complete Z_2^3 classification scheme.

Contribution

It introduces six new interacting topological insulators in three dimensions and proves that these, along with known phases, form a complete classification.

Findings

Identified 6 new topological insulators with no non-interacting analogs

Classified all phases using a Z_2^3 group structure

Discussed experimental signatures for the new phases

Abstract

A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic topological insulators that have no non-interacting counterpart. Combined with the previously known band-insulators, these produce a total of 8 topologically distinct phases. Two of the new topological insulators have a simple physical description as Mott insulators in which the electron spins form spin analogs of the familiar topological band-insulator. The remaining are obtained as combinations of these two `topological paramagnets' and the topological band insulator. We prove that these 8 phases form a complete list of all possible interacting topological insulators, and are classified by a Z_2^3 group-structure. Experimental signatures are also discussed for these phases.