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

Interaction effect on topological classification of superconductors in two dimensions