Exact Results in Quantum Theory

I will discuss the properties of topological insulators (TIs), existing in two-dimensional (2D) and three-dimensional (3D) material systems. In general, they are characterized by an energy gap in the bulk electronic band structure and the presence of metallic states on their surfaces or edges. Closing the bulk band gap by the surface or edge states is caused by the nontrivial topology of the bulk states, characterized by nonzero topological invariants. The examples will be narrowed to the recently discussed nitrites based quantum wells which display a behaviour surprisingly different from typical topological insulators.