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Motivated by recent progress in crystalline symmetry protected topological(SPT) phases of interacting bosons, we study topological crystallineinsulators/superconductors (TCIs) of strongly interacting fermions. Weconstruct a class of intrinsically interacting fermionic TCIs, and show thatthey are beyond both free-fermion TCIs and bosonic crystalline SPT phases. Wealso show how these phases can be characterized by symmetry protected gaplessfermion modes on the corners/hinges of an open system.

Intrinsically interacting topological crystalline insulators and superconductors