Construction and classification of crystalline topological superconductor and insulators in three-dimensional interacting fermion systems

Abstract

The natural existences of crystalline symmetry in real materials manifest the importance of understanding crystalline symmetry protected topological(SPT) phases, especially for interacting systems. In this paper, we systematically construct and classify all the crystalline topological superconductors and insulators in three-dimensional (3D) interacting fermion systems using the novel concept of topological crystal. The corresponding higher-order topological surface theory can also be systematically studied via higher-order bulk-boundary correspondence. In particular, we discover an intriguing fact that almost all topological crystals with nontrivial 2D block-states are intrinsically interacting topological phases that cannot be realized in any free-fermion systems. Moreover, the crystalline equivalence principle for 3D interacting fermionic systems is also verified, with an additional subtle "twist" on the spin of fermions.

Fractional second-order topological insulator from a three-dimensional coupled-wires construction

“…While the original theory of HOTIs builds on singleparticle band structure considerations, it is interesting to ask whether there are exotic interaction-driven HOTI phases that do not fit into this conventional picture. While this question has by now been answered affirmatively [45][46][47][48][49][50][51][52][53], concrete toy models for strongly interacting HOTI phases are still extremely rare since analytical tools to study interacting systems in more than one dimension are scarce. One way forward is offered by the so-called coupled-wires approach [54,55], where a twodimensional (2D) or three-dimensional (3D) system is modeled as an array of weakly coupled one-dimensional (1D) wires.…”