A new class of $(2+1)$-d topological superconductor with $\mathbb{Z}_8$ topological classification

TL;DR

This paper introduces a new class of (2+1)-dimensional topological superconductors with time-reversal and spin conservation symmetries, revealing a $$ classification under interactions, expanding understanding of interacting topological phases.

Contribution

It identifies a novel class of topological superconductors with a $$ classification in the presence of interactions, contrasting with the non-interacting $$ classification.

Findings

Topological superconductors in this class are classified by  with interactions.

Without interactions, the classification is .

The study advances understanding of interacting topological phases in 2+1 dimensions.

Abstract

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.