Interaction effect on topological classification of superconductors in two dimensions

TL;DR

This paper introduces a new class of 2D superconductors with specific symmetries and shows that their topological classification changes from an integer to a mod 8 value when interactions are considered, highlighting the impact of interactions on topological phases.

Contribution

The study reveals how interactions alter the topological classification of 2D superconductors with mirror and time-reversal symmetry from  to 8, a novel insight into topological matter.

Findings

Topological classification changes from  to 8 with interactions.

Interactions have a qualitative effect on topological states.

New class of 2D superconductors with specific symmetries introduced.

Abstract

We introduce a new class of superconductors (SCs) in two spatial dimensions with time reversal symmetry and reflection (i.e., mirror) symmetry. In the absence of interactions, topological classes of these SCs are distinguished by an integer-valued ($\mathbb{Z}$) topological invariant. When interactions are included, we show that the topological classification is modified to $\mathbb{Z}_8$. This clearly demonstrates that interactions can have qualitative effect on topological classifications of gapped states of matter in more than one dimension.