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

We study theoretically two-dimensional single-crystalline sheets of semiconductors that form 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 rocksalt 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 nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial 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 pi-pi* 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.Comment: 12 pages, 12 figure

Topological states in multi-orbital HgTe honeycomb lattices

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.Comment: includes supplementary materia

Electrical transport through self-assembled colloidal nanomaterials and their perspectives

Colloidal nanoparticles developed as interesting objects to establish two- or three-dimensional super-structures with properties not known from conventional bulk materials. Beyond, the properties can be tuned and quantum effects can be exploited. This allows understanding electronic and optoelectronic transport phenomena and developing corresponding devices. The state-of-the-art in this field will be reviewed and possible challenges and prospects will be identified.Comment: 8 pages. arXiv admin note: text overlap with arXiv:1501.0236

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

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Electronic structure of atomically coherent square semiconductor superlattices with dimensionality below two

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 (2013)], 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.QN/Quantum NanoscienceApplied Science

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

We study theoretically two-dimensional single-crystalline sheets of semiconductors that form 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 rocksalt 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 nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial 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