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

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.

Figures (1)

• Figure 1: (a) Illustration of the T-breaking mass domain wall along the edge of the 2d TSC. The mass is induced by a proximity effect of the TSC with an $s$-wave superconductor, and the mass domain wall corresponds to a Josephson junction between two such $s$-wave superconductors (see text). (b) Illustration of a strip of 2d TSC with the edge states on the two edges gapped by opposite mass terms $m$ and $-m$, which is topologically equivalent to a 1d TSC in the BDI class, with Majorana zero modes at the end. (c) Illustration that a sphere with two topological defects is equivalent to a cylinder with periodic boundary condition.