Room-temperature quantum spin Hall effect in HgTe honeycomb superlattices*

The recent experimental realization of self-assembled honeycomb superlattices of truncated semiconducting nanocrystals has opened a new path to engineer graphene-like structures. Atomistic band-structure calculations for honeycomb lattices of PbSe and CdSe have shown a rich band structure, with Dirac cones at the $s$- as well as at the $p$-bands, in addition to a flat $p$-band. By controlling the chemical composition of the nanocrystals, lattices with strong spin-orbit coupling can be artificially designed. We show that for HgTe a huge non-trivial gap, of order of 50 meV, opens at the K-points. We calculate the edge states using both, an atomistic calculation that takes into account $10^6$ atomic orbitals per unit cell, as well as an effective 16-bands tight-binding model, and find that the quantum spin Hall effect should be observable in this material at temperatures of the order of room temperature.