Theory of surface phenomena in topological insulators

Recently discovered topological insulators (TIs) are materials with bulk bandgap and robust gapless surface states protected by topological invariants that characterize their bulk band structure. After a brief introduction to the physics of TIs I will describe recent theoretical advances in understanding the behavior of surface electrons in the presence of both magnetic and non-magnetic impurities, surface steps, as well as magnetic and superconducting coating. The key property of the topological surface states -- absence of backscattering from non-magnetic defects -- leads to a number of features that stand in a stark contrast to the physics of ordinary non-topological states. Among these are vastly enhanced transmission through crystal steps, absence of quasiparticle interference patterns caused by non-magnetic impurities and formation of a gap in the presence of magnetic impurities.