We study theoretically two-dimensional single-crystalline sheets of semiconductors forming a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rock-salt Pb-chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nano-geometry leads to rich band structures including, in the conduction band, Dirac cones at two distinct energies and non-trivial flat bands, and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the π − π ⋆ band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene, they combine a Dirac cone and flat bands because of their P -orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals.

Research on graphene has revealed remarkable phenomena arising in the honeycomb lattice. However, the quantum spin Hall effect predicted at the K point could not be observed in graphene and other honeycomb structures of light elements due to an insufficiently strong spin–orbit coupling. Here we show theoretically that 2D honeycomb lattices of HgTe can combine the effects of the honeycomb geometry and strong spin–orbit coupling. The conduction bands, experimentally accessible via doping, can be described by a tight-binding lattice model as in graphene, but including multi-orbital degrees of freedom and spin–orbit coupling. This results in very large topological gaps (up to 35 meV) and a flattened band detached from the others. Owing to this flat band and the sizable Coulomb interaction, honeycomb structures of HgTe constitute a promising platform for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase.

The electronic structure of recently synthesized square superlattices with atomic coherence composed of PbSe, CdSe, or CdTe nanocrystals (NCs) attached along {100} facets is investigated using tight-binding calculations. In experimental realizations of these systems [W. H. Evers et al., Nano Lett. 13, 2317], NC facets are atomically bonded, resulting in single-crystalline sheets, which, due to their nanogeometry, have an effective dimensionality below two. We predict electronic structures composed of successive bands formed by strong coupling between the wave functions of nearest-neighbor NCs. This coupling is mainly determined by the number of atoms at the NC bonding plane. The band structures deviate markedly from that of the corresponding two-dimensional (2D) quantum well; the 2D case can be recovered, however, if the effects of the nanogeometry are gradually reduced. The width of the bands can reach hundreds of meV, ascribing highly promising transport properties to square superlattices. The band edges are located at k = 0 except for PbSe superlattices, where their position in k space surprisingly depends on the parity of the number of {100} atomic planes in the NCs. Our calculations demonstrate that semiconductors with dimensionality below two have a strong potential for (opto-)electronic, photovoltaic, and spintronic applications.

GaN quantum dots (QDs) grown in semipolar (112¯2) AlN by plasma-assisted molecular-beam epitaxy were studied by transmission electron microscopy (TEM) and scanning transmission electron microscopy techniques. The embedded (112¯2)-grown QDs exhibited pyramidal or truncated-pyramidal morphology consistent with the symmetry of the nucleating plane, and were delimited by nonpolar and semipolar nanofacets. It was also found that, in addition to the (112¯2) surface, QDs nucleated at depressions comprising {101¯1} facets. This was justified by ab initio density functional theory calculations showing that such GaN/AlN facets are of lower energy compared to (112¯2). Based on quantitative high-resolution TEM strain measurements, the three-dimensional QD strain state was analyzed using finite-element simulations. The internal electrostatic field was then estimated, showing small potential drop along the growth direction, and limited localization at most QD interfaces.

We perform a detailed analysis of the valence band splitting (VBS) effect on the absorption spectra of monoclinic Cu2(Sn,Ge,Si)S3 combining theory and experiment. We calculate the imaginary part of the dielectric function for all three compounds using hybrid functionals and maximally localized Wannier functions in remarkably dense k ‐meshes to ensure an accurate description of the low energy spectral regime. We find that the VBS will affect the absorption spectra of these materials leading to multiple absorption onsets. Our experimental spectra on Cu2(Sn,Ge)S3, analysed using both Tauc plots and inflection points, verify this prediction. A good agreement between theory and experiment in terms of VBS values is recorded. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

The open issue of the n-type conductivity and its correlation to threading dislocations (TDs) in InN is addressed through first principles calculations on the electronic properties of a-edge TDs. All possible dislocation core models are considered (4-, 5/7-, and 8-atom cores) and are found to modify the band structure of InN in a distinct manner. In particular, nitrogen and indium low coordinated atoms in the eight-atom core induce states near the valence band maximum and above the conduction band minimum, respectively. The formation of a nitrogen–nitrogen “wrong” bond is observed at the 5/7-atom core resulting in a state inside the band gap. The 4- and 5/7-atom cores induce occupied states resonant in the conduction band due to In–In strain induced interactions and wrong bonds, respectively. These occupied states designate TDs as a source of higher electron concentrations in InN and provide direct evidence that TDs contribute to its inherent n-type conductivity.

The structures and energies of {0001} interfaces between GaN and AlN are studied by both ab initio methods and molecular dynamics using the Tersoff empirical inter‐atomic potential. Based on experimental observations, structural configurations depending on polarity and atomic stacking are considered. It is evidenced by both ab initio and empirical calculations that III‐polar interfaces are energetically favourable compared to the N‐polar. In addition, the ab initio analysis shows that the wurtzite interfacial stacking is energetically preferable compared to zinc blende. A linear dependence between the bandgap energy and the strain in AlN/GaN heterostructures is found. It is shown that the bandgap increases with increasing c/a ratio while an inverse proportionality relationship is observed in the case of lattice parameter a. However, biaxial strain is found to flatten this variation considerably. Empirical potential calculations yield the interfacial energies, taking into account the relaxation of the lattice mismatch due to arrays of misfit dislocations and in combination with ab initio methods estimate that the energetically favourable III polarity interface exhibits at least 18% larger critical thickness than the N polar.

Density functional theory calculations were performed on undoped AlN screw threading dislocations (TDs) as well as TDs doped by indium and oxygen, prompted by integrated experiments through transmission electron microscopy and spectroscopic techniques demonstrating enhanced In and O concentrations in screw dislocation cores. It is revealed that screw TDs act as conduction pathways to charge carriers, introducing multiple levels in the bandgap due to overstrained, dangling, and “wrong” bonds formed even in the undoped cores. The presence of impurities and especially metallic In elevates the metal-like electronic structure of the distorted material and promotes the conductivity along the dislocation line. Hence screw dislocations in AlN are established as highly prominent conductive nanowires in semiconducting thin films and prospects for novel, highly functional nano-device materials through exploitation of screw TDs are attested.