- 2250 Elings Hall
In this talk I will discuss how information about topology of a solid state (cold atom) system can be extracted by means of Wannier functions. I will first introduce the method for computing topological invariants of insulating band structures and illustrate it with applications to real materials. I will then show that this method, being purely numerical in the solid state context, can be simulated experimentally in the context of cold atoms. It solves the problem of measuring topological indices of artificial band structures realized in optical lattices in a straightforward manner. Time permitting I will discuss the issue of topological obstruction that appears in Z_2 topological insulators and I will describe an explicit procedure to construct Bloch states that are globally smooth on the Brillouin zone torus, thus allowing one to construct exponentially localized Wannier functions for these insulators.