Crystalline Topological Insulators and Superconductors: Classification and Bulk-Boundary Correspondence

Event Date: 

Tuesday, June 9, 2015 - 4:00pm

Event Location: 

  • Broida 1640


Shinsei Ryu, University of Illinois, Urbana-Champaign



The importance of an interplay between topology and symmetries in solid state physics has been recognized over years since the discoveries of time-reversal symmetric topological insulators. While initially the effects of non-spatial ("on-site") symmetry such as time-reversal symmetry have been studied, it has been becoming clear that spatial symmetries such as reflection symmetry and point group symmetries also give rise to interesting topological phases of matter, including “crystalline topological insulators”. More generally, symmetry-protected topological phases(SPT phases) of matter, i.e., phases of matter that are not adiabatically connected to a trivial phase such as an atomic insulator once a symmetry condition is enforced, has been widely discussed.

In this talk, I plan to discuss phases of matter with reflection symmetry (parity symmetry) with and without interactions. For non-interacting fermion systems, I will discuss a systematic classification of topological phases in a manner similar to the periodic table of topological insulators and superconductors (also known as “10-fold way”). While a systematic analysis is possible for non-interacting fermions, an important challenge is to understand the effects of strong electron correlations. To get some insight into this problem, I will discuss an example where by the effects of interactions the non-interacting classification breaks down. In particular, to diagnose the effects of interactions, I will propose a generalization of Laughlin's thought experiment to SPT phase protected by reflection symmetry, by making use of the bulk-boundary correspondence of topological states of matter.