We present here the minimal tight-binding model for a single layer of transition metal dichalcogenides (TMDCs) MX2 (M-metal, X-chalcogen) which illuminates the physics and captures band nesting, massive Dirac Fermions and Valley Lande and Zeeman magnetic field effects. TMDCs share the hexagonal lattice with graphene but their electronic bands require much more complex atomic orbitals. Using symmetry arguments, a minimal basis consisting of 3 metal d-orbitals and 3 chalcogen dimer p-orbitals is constructed. The tunneling matrix elements between nearest neighbor metal and chalcogen orbitals are explicitly derived at K, −K and Γ points of the Brillouin zone. The nearest neighbor tunneling matrix elements connect specific metal and sulfur orbitals yielding an effective 6 × 6 Hamiltonian giving correct composition of metal and chalcogen orbitals but not the direct gap at K points. The direct gap at K, correct masses and conduction band minima at Q points responsible for band nesting are obtained by inclusion of next neighbor Mo-Mo tunneling. The parameters of the next nearest neighbor model are successfully fitted to MX2 (M=Mo, X=S) density functional (DFT) ab-initio calculations of the highest valence and lowest conduction band dispersion along K −Γ line in the Brillouin zone. The effective two-band massive Dirac Hamiltonian for MoS2, Lande g-factors and valley Zeeman splitting are obtained.

We discuss here the effect of band nesting and topology on the spectrum of excitons in a single layer of MoS2, a prototype transition metal dichalcogenide material. We solve for the single particle states using the ab initio based tight-binding model containing metal d and sulfur p orbitals. The metal orbitals contribution evolving from K to Γ points results in conduction-valence band nesting and a set of second minima at Q points in the conduction band. There are three Q minima for each K valley. We accurately solve the Bethe-Salpeter equation including both K and Q points and obtain ground and excited exciton states. We determine the effects of the electron-hole single particle energies including band nesting, direct and exchange screened Coulomb electron-hole interactions and resulting topological magnetic moments on the exciton spectrum. The ability to control different contributions combined with accurate calculations of the ground and excited exciton states allows for the determination of the importance of different contributions and a comparison with effective mass and k · p massive Dirac fermion models.

We present here results of atomistic theory of electrons confined by metallic gates in a single layer of transition metal dichalcogenides. The electronic states are described by the tight-binding model and computed using a computational box including up to million atoms with periodic boundary conditions and parabolic confining potential due to external gates embedded in it. With this methodology applied to MoS2, we find a twofold degenerate energy spectrum of electrons confined in the two non-equivalent K-valleys by the metallic gates as well as six-fold degenerate spectrum associated with Q-valleys. We compare the electron spectrum with the energy levels of electrons confined in GaAs/GaAlAs and in self-assembled quantum dots. We discuss the role of spin splitting and topological moments on the K and Q valley electronic states in quantum dots with sizes comparable to experiment. arXiv:1907.09512v1 [cond-mat.mes-hall]

No abstract

We determine here the evolution of the bandgap energy with size in graphene quantum dots (GQDs). We find oscillatory behaviour of the bandgap and explain its origin in terms of armchair and zigzag edges. The electronic energy spectra of GQDs are computed using both the tight binding model and ab initio density functional methods. The results of the tight binding model are analyzed by dividing zigzag graphene quantum dots into concentric rings. For each ring, the energy spectra, the wave functions and the bandgap are obtained analytically. The effect of inter-ring tunneling on the energy gap is determined. The growth of zigzag terminated GQD into armchair GQD is shown to be associated with the addition of a one-dimensional Lieb lattice of carbon atoms with a shell of energy levels in the middle of the energy gap of the inner zigzag terminated GQD. This introduces a different structure of the energy levels at the bottom of the conduction and top of the valence band in zigzag and armchair GQD which manifests itself in the oscillation of the energy gap with increasing size. The evolution of the bandgap with the number of carbon atoms is compared with the notion of confined Dirac Fermions and tested against ab initio calculations of Kohn-Sham and TD-DFT energy gaps.