NBIA CMT Seminar: Vladimir Juricic (Utrecht)
Topological band insulators are bulk insulating states of matter, which in the presence of time-reversal symmetry feature metallic states at their edge or surface. This state of quantum matter has been recently experimentally realized in the HgTe/CdTe quantum wells and various (mostly) Bismuth-based compounds.
I will first introduce the concept of topological band insulators and then discuss the role of crystal symmetries in the physics of these states of quantum matter. I will derive the classification of topological band-insulators protected not only by time-reversal, but also by space group symmetries . I will show that there are three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley (crystalline) topological insulators sensitive to both elastic and crystalline disorder.
I will show how some of these states can be realized when Bernevig-Hughes-Zhang tight-binding model, originally introduced for the HgTe/CdTe quantum wells, is generalized to include longer-range hoppings. I will also discuss probing of the topological states in the bulk by magnetic pi-fluxes and lattice dislocations both in two  and three dimensions . Finally, I will consider some experimental implications of our classification scheme.
 R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, Nature Physics 9, 98 (2013).
 V. Juricic, A. Mesaros, R.-J. Slager, and J. Zaanen, Phys. Rev. Lett. 108, 106403 (2012).
 R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, arXiv: 1401.4044.