Interaction effect on topological classification of superconductors in two dimensions

We introduce a 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 a qualitative effect on topological classifications of gapped states of matter in more than one dimension.