## SCL Seminar by Vladimir Juricic

Dr Vladimir Juricic from University of Leiden visited SCL and presented a seminar:

"The Space Group Classification of Topological Band-Insulators"

Abstract:

Topological band insulators are bulk insulating states of matter which in the presence of time-reversal invariance feature metallic states at their edge or surface [1]. This state of quantum matter has been recently experimentally realized in the HgTe quantum wells.

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 [2]. 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 non-topological and crystalline disorder. I will show how some of these states can be realized in two dimensions when the tight-binding M-B model, originally introduced for the HgTe quantum wells, is generalized to include longer-range hoppings. I will also discuss probing of these states by magnetic pi-fluxes and lattice dislocations [3]. Finally, I will consider some experimental implications of our classification scheme.

[1] For recent reviews, see M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010); X. L. Qi and S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).

[2] R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, Nature Physics 9, 98 (2013).

[3] V. Juricic, A. Mesaros, R.-J. Slager, and J. Zaanen, Phys. Rev. Lett. 108, 106403 (2012).