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We study theoretically two-dimensional single-crystalline sheets ofsemiconductors that form a honeycomb lattice with a period below 10 nm. Thesesystems could combine the usual semiconductor properties with Dirac bands.Using atomistic tight-binding calculations, we show that both the atomiclattice and the overall geometry influence the band structure, revealingmaterials with unusual electronic properties. In rocksalt Pb chalcogenides, theexpected Dirac-type features are clouded by a complex band structure. However,in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycombnanogeometry leads to rich band structures, including, in the conduction band,Dirac cones at two distinct energies and nontrivial flat bands and, in thevalence band, topological edge states. These edge states are present in severalelectronic gaps opened in the valence band by the spin-orbit coupling and thequantum confinement in the honeycomb geometry. The lowest Dirac conduction bandhas S-orbital character and is equivalent to the pi-pi* band of graphene butwith renormalized couplings. The conduction bands higher in energy have nocounterpart in graphene; they combine a Dirac cone and flat bands because oftheir P-orbital character. We show that the width of the Dirac bands variesbetween tens and hundreds of meV. These systems emerge as remarkable platformsfor studying complex electronic phases starting from conventionalsemiconductors. Recent advancements in colloidal chemistry indicate that thesematerials can be synthesized from semiconductor nanocrystals.

Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry