In this talk, I will describe a few properties of new phases of condensed matter called topological insulators. These phases are analogous to the quantum Hall effects, in particular they have a bulk energy gap as ordinary insulators. However, these insulators are characterized by a topological order which implies the existence of robust edges states. In the case of the Quantum Hall Effect, these edge states are chiral modes, reflecting the breaking of time reversal symmetry. In these new topological insulators, time reversal symmetry is preserved, and these edges modes consists of (Kramers) pairs of states propagating in opposite directions.
I will describe two recent examples of topological insulators and their experimental realization : the two dimensional Quantum Spin Hall Effect found recently in HgTe quantum well, and the three dimensional phases discovered recently in a class of materials including Bi2Se3, Bi2Te3, Sb2Te3.
