Interacting fermionic topological insulators/superconductors in three dimensions

TL;DR

This paper classifies three-dimensional interacting fermionic topological insulators and superconductors with various symmetries, revealing their stability, surface states, and the role of interactions in their topological properties.

Contribution

It provides a comprehensive classification of 3D fermionic SPT phases with interactions, extending free fermion results and exploring surface states with topological order.

Findings

Classification of 3D fermionic SPT phases for all symmetry classes

Identification of stable phases under interactions

Description of surface states with intrinsic topological order

Abstract

Symmetry Protected Topological (SPT) phases are a minimal generalization of the concept of topological insulators to interacting systems. In this paper we describe the classification and properties of such phases for three dimensional(3D) electronic systems with a number of different symmetries. For symmetries representative of all classes in the famous 10-fold way of free fermion topological insulators/superconductors, we determine the stability to interactions. By combining with results on bosonic SPT phases we obtain a classification of electronic 3D SPT phases for these symmetries. In cases with a normal U(1) subgroup we show that this classification is complete. We describe the non-trivial surface and bulk properties of these states. In particular we discuss interesting correlated surface states that are not captured in a free fermion description. We show that in many, but not all cases, the surface can be gapped while preserving symmetry if it develops intrinsic topological order.