Topological States in Multi-Orbital Honeycomb Lattices of HgTe (CdTe) Quantum Dots

We summarize recent theoretical works on artificial graphene realized by honeycomb lattices of semiconductor (CdSe, HgTe, CdTe) quantum dots forming a two-dimensional single-crystalline sheet. In the case of CdSe, we predict conduction bands with Dirac cones at two distinct energies and nontrivial flat bands. An analogous behavior is found in HgTe but, in addition, the strong spin-orbit coupling opens large topologically nontrivial gaps, leaving a flattened band detached from the others. We deduce that honeycomb lattices of HgTe quantum dots may constitute promising platforms for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase. Similar predictions are made for CdTe but with smaller nontrivial gaps.