Low dimensional semiconductors have been extensively investigated during the past few decades due to the abundance of their applications, such as transistors, solar cells, photo-detectors, light emitting diodes and lasers. An alternative perspective to this field, which is traditionally dominated by III-V and II-VI materials grown by gas phase methods in high vacuum, could stem from the oriented attachment of colloidal nanocrystals (NCs). The recently reported formation of chalcogenide-based, square or honeycomb superlattices through NCs oriented attachment  could open new pathways to the exploitation of low dimensional systems and hence necessitates determination of their electronic properties.
In the current contribution, we present results of tight binding calculations on the electronic structure of single-crystalline sheets, with an effective dimensionality below two, and graphene- / silicene- like superlattices of PbSe or CdSe NCs [2, 3]. The primary role of both the atomic lattice and the overall geometry on the band structure is evident in all cases. The strong coupling between the wave functions of nearest-neighbor NCs, mainly determined by the number of atoms at the NCs bonding plane, results in electronic structures composed of successive bands. For single-crystalline sheets, band structures markedly differentiate from that of corresponding two-dimensional quantum wells, but the latter can be recovered if nanogeometry effects are gradually reduced. The enhanced width of the bands ascribes highly promising transport properties to square superlattices .
In the case of honeycomb lattices, which could combine the usual semiconductor properties with Dirac bands, unusual electronic properties are revealed. In rock-salt PbSe, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende CdSe, the honeycomb nanogeometry leads to band structures which comprise Dirac cones at two distinct energies and non-trivial flat bands in the conduction band whereas in the valence band several bands with topological edge states are present. These systems could serve as platforms for studying complex electronic phases starting from conventional semiconductors .
Acknowledgment: This work has been supported by funding of the French National Research Agency (ANR-09-BLAN-0421-01)
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