Topological Insulators

Defined by the fact that they have conducting states on the edges but not in the bulk. This comes from the fact that having a non-trivial topological invariant \(n\neq 0\) on the bulk of the material and the vacuum having \(n=0\).

Topological Crystalline Insulator

Class of TIs protected by their crystal symmetry

Time reversal Topological Insulator

Class of TIs characteried by a \(Z_2\) cyclic group (i.e. takes values of 0 and 1, all two-element group is isomorphic to \(Z_2\))