Condensed Matter Theory Seminar: Dr. Jian-Hao Zhang - Penn State University: Construction and classification of crystalline topological superconductors and insulators in three-dimensional interacting fermion systems

Abstract: The natural existences of crystalline symmetry in the single crystals of real materials manifest the importance of investigating the crystalline topological phases in various spatial dimensions. In this talk, I will systematically construct and classify the crystalline symmetry-protected topological (SPT) phases in three-dimensional (3D) interacting fermionic systems by explicit topological crystals in real space. Based on topological crystals, their 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.