  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.
