Topological states in multi-orbital HgTe honeycomb lattices

Research on graphene has revealed remarkable phenomena arising in the honeycomb lattice. However, the quantum spin Hall effect predicted at the K point could not be observed in graphene and other honeycomb structures of light elements due to an insufficiently strong spin–orbit coupling. Here we show theoretically that 2D honeycomb lattices of HgTe can combine the effects of the honeycomb geometry and strong spin–orbit coupling. The conduction bands, experimentally accessible via doping, can be described by a tight-binding lattice model as in graphene, but including multi-orbital degrees of freedom and spin–orbit coupling. This results in very large topological gaps (up to 35 meV) and a flattened band detached from the others. Owing to this flat band and the sizable Coulomb interaction, honeycomb structures of HgTe constitute a promising platform for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase. The observation of the quantum spin Hall effect in graphene is hindered by weak spin–orbit coupling. Here, Beugeling et al . demonstrate how topological phases may be realized in analogous artificial HgTe nanocrystal honeycomb lattices with strong spin–orbit coupling and multi-orbital ordering.