Interaction-enabled topological crystalline phases

In this article we provide a general mechanism for generating interaction-enabled fermionic topological phases. We illustrate the mechanism with crystalline symmetry-protected topological phases in one, two, and three spatial dimensions. These nontrivial phases require interactions for their existence, and in the cases we consider, the free-fermion classification yields only a trivial phase. For the one- and two-dimensional phases we consider, we provide explicit exactly solvable models which realize the interaction-enabled phases. Similar to the interpretation of the Kitaev Majorana wire as a mean-field p-wave superconductor Hamiltonian arising from an interacting model with quartic interactions, we show that our systems can be interpreted as "mean-field" charge-4e superconductors arising, e.g., from an interacting model with eight-body interactions or through another physical mechanism. The quartet superconducting nature allows for the teleportation of full Cooper pairs and, in two dimensions, for interesting semiclassical crystalline defects with non-Abelian anyon bound states.