|
The existing classification of topological band insulators departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. I will discuss the classification of topological band insulators protected not only by time-reversal, but also by crystalline symmetries [1]. We find 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 topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional topological band insulators. I will discuss how some of these topological states can be realized in two dimensions when tight-binding M-B model, originally introduced for HgTe quantum wells, is generalized to include longer-range hoppings. I will then show that two-dimensional topological states can be probed by pi-fluxes and dislocations [2]. Finally, I will consider some experimental implicationsof our classification scheme.
References: [1] R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, Nature Physics 9, 98 (2013). [2] V. Juricic, A. Mesaros, R.-J. Slager, and J. Zaanen, Phys. Rev. Lett. 108, 106403 (2012). |
|