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The construction and classification of crystalline symmetry protectedtopological (SPT) phases in interacting bosonic and fermionic systems have beenintensively studied in the past few years. Crystalline SPT phases are not onlyof conceptual importance, but also provide great opportunities towardsexperimental realization since space group symmetries naturally exist for anyrealistic material. In this paper, we systematically classify the crystallinetopological superconductors (TSC) and topological insulators (TI) in 2Dinteracting fermionic systems by using an explicit real-space construction. Inparticular, we discover an intriguing fermionic crystalline topologicalsuperconductor that can only be realized in interacting fermionic systems(i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verifythe recently conjectured crystalline equivalence principle for generic 2Dinteracting fermionic systems.

Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems