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The interest in 2-dimensional systems with a honeycomb lattice and related Dirac-type electronic bands has exceeded the prototype graphene1. Currently, 2-dimensional atomic2,3 and nanoscale4-8 systems are extensively investigated in the search for materials with novel electronic properties that can be tailored by geometry. The immediate question that arises is how to fabricate 2-D semiconductors that have a honeycomb nanogeometry, and as a consequence of that, display a Dirac-type band structure? Here, we show that atomically coherent honeycomb superlattices of rocksalt (PbSe, PbTe) and zincblende (CdSe, CdTe) semiconductors can be obtained by nanocrystal self-assembly and facet-to-facet atomic bonding, and subsequent cation exchange. We present a extended structural analysis of atomically coherent 2-D honeycomb structures that were recently obtained with self-assembly and facet-to-facet bonding9. We show that this process may in principle lead to three different types of honeycomb structures, one with a graphene type-, and two others with a silicene-type structure. Using TEM, electron diffraction, STM and GISAXS it is convincingly shown that the structures are from the silicene-type. In the second part of this work, we describe the electronic structure of graphene-type and silicene type honeycomb semiconductors. We present the results of advanced electronic structure calculations using the sp3d5s* atomistic tight-binding method10. For simplicity, we focus on semiconductors with a simple and single conduction band for the native bulk semiconductor. When the 3-D geometry is changed into 2-D honeycomb, a conduction band structure transformation to two types of Dirac cones, one for S- and one for P-orbitals, is observed. The width of the bands depends on the honeycomb period and the coupling between the nanocrystals. Furthermore, there is a dispersionless P-orbital band, which also forms a landmark of the honeycomb structure. The effects of considerable intrinsic spin-orbit coupling are briefly considered. For heavy-element compounds such as CdTe, strong intrinsic spin-‐orbit coupling opens a non-trivial gap at the P-orbital Dirac point, leading to a quantum Spin Hall effect10-12. Our work shows that well known semiconductor crystals, known for centuries, can lead to systems with entirely new electronic properties, by the simple action of nanogeometry. It can be foreseen that such structures will play a key role in future opto-electronic applications, provided that they can be fabricated in a straightforward way.
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