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The classification of topological states of matter depends on spatialdimension and symmetry class. For non-interacting topological insulators andsuperconductors the topological classification is obtained systematically andnontrivial topological insulators are classified by either integer or $Z_2$.The classification of interacting topological states of matter is much morecomplicated and only special cases are understood. In this paper we study a newclass of topological superconductors in $(2+1)$ dimensions which hastime-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. Wedemonstrate that the superconductors in this class is classified by$\mathbb{Z}_8$ when electron interaction is considered, while theclassification is $\mathbb{Z}$ without interaction.

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