Topological insulator

Summary

A topological insulator is a material that is insulating in its interior but conducts along its boundary. The reason is that its occupied electron bands carry a nontrivial topological invariant. In the narrow sense it is a time-reversal-invariant insulator of spin-$1/2$ electrons with a nontrivial $\Z_2$ invariant. This $\Z_2$ invariant was introduced by Charles Kane and Eugene Mele in 2005. The invariant cannot change without closing the bulk energy gap or breaking the symmetry, and it forces gapless states on the surface. The integer quantum Hall states, with their TKNN invariant, are the earlier example without time-reversal symmetry.