Quantum spin Hall systems and topological insulators

Topological insulators (quantum spin Hall systems) are insulating in the bulk but have gapless edge/surface states, which remain gapless even when nonmagnetic disorder or interaction is present. This robustness stems from the topological nature characterized by the Z 2 topological number, and this offers us various kinds of new novel properties. We review prominent advances in theories and in experiments on topological insulators since their theoretical proposal in 2005.