  The construction and classification of crystalline symmetry protected
topological (SPT) phases in interacting bosonic and fermionic systems have been
intensively studied in the past few years. Crystalline SPT phases are not only
of conceptual importance, but also provide great opportunities towards
experimental realization since space group symmetries naturally exist for any
realistic material. In this paper, we systematically classify the crystalline
topological superconductors (TSC) and topological insulators (TI) in 2D
interacting fermionic systems by using an explicit real-space construction. In
particular, we discover an intriguing fermionic crystalline topological
superconductor that can only be realized in interacting fermionic systems
(i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify
the recently conjectured crystalline equivalence principle for generic 2D
interacting fermionic systems.
