Topological insulators in the presence of interactions

Stephan Rachel

Time-reversal invariant topological insulators - bulk insulators with protected metallic edges or surfaces - are characterized by a Z2 invariant and cannot be adiabatically connected to trivial band insulator phases unless the single particle gap closes. While Z2 topological insu- lators are robust against disorder, rigorous and general results about the fate of topological insulators in the presence of prominent electron-electron interactions are limited. In this talk, we discuss the effect of electron-electron interactions in a two-dimensional topo- logical insulator (as realized by the Kane-Mele model on the honeycomb lattice) and work out the phase diagram analytically and numerically. For intermediate interactions, the possible existence of more exotic phases such as spin liquids, topological Mott insulators, and even topologically ordered phases is discussed. Finally, we show that breaking of axial spin- symmetry may affect our results at all interaction scales.