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We present here the minimal tight--binding model for a single layer of transition metal dichalcogenides (TMDCs) MX$_{2}$ (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 $Gamma$ points of the Brillouin zone. The nearest neighbor tunneling matrix elements connect specific metal and sulfur orbitals yielding an effective $6times 6$ 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 MX$_2$ (M=Mo, X=S) density functional (DFT) ab--initio calculations of the highest valence and lowest conduction band dispersion along $K-Gamma$ line in the Brillouin zone. The effective two--band massive Dirac Hamiltonian for MoS$_2$, Lande g--factors and valley Zeeman splitting are obtained.
We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides $MX_2$ ($M$=Mo, W; $X$=S, Se, Te). As the conduction and valence band edges are predominantly contribut
Monolayer transition metal dichalcogenides $MX_2$ ($M$ = Mo,W and $X$ = Te, Se, S) in 1T structure were predicted to be quantum spin Hall insulators based on first-principles calculations, which were quickly confirmed by multiple experimental groups.
This paper presents a theoretical description of both the valley Zeeman effect (g-factors) and Landau levels in two-dimensional H-phase transition metal dichalcogenides (TMDs) using the Luttinger-Kohn approximation with spin-orbit coupling. At the va
We present an accurate textit{ab-initio} tight-binding hamiltonian for the transition-metal dichalcogenides, MoS$_2$, MoSe$_2$, WS$_2$, WSe$_2$, with a minimal basis (the textit{d} orbitals for the metal atoms and textit{p} orbitals for the chalcogen
The kagome lattice is a two-dimensional network of corner-sharing triangles known as a platform for exotic quantum magnetic states. Theoretical work has predicted that the kagome lattice may also host Dirac electronic states that could lead to topolo