Band nesting, massive Dirac Fermions and Valley Lande and Zeeman effects in transition metal dichalcogenides: a tight-binding model

Abstract

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 $6\times 6$ 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.

References in corpus (43)

• Atomically thin MoS2: A new direct-gap semiconductor
• Van der Waals heterostructures
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Control of valley polarization in monolayer MoS2 by optical helicity
• Valley polarization in MoS2 monolayers by optical pumping
• MoS_2 as an ideal material for valleytronics: valley-selective circular dichroism and valley Hall effect
• Valley contrasting physics in graphene: magnetic moment and topological transport
• How does quantum confinement influence the electronic structure of transition metal sulfides TmS2
• Electrical Control of Two-Dimensional Neutral and Charged Excitons in a Monolayer Semiconductor
• Optical Generation of Excitonic Valley Coherence in Monolayer WSe2
• Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2
• Tightly bound excitons in monolayer WSe2
• k.p theory for two-dimensional transition metal dichalcogenide semiconductors
• Probing Excitonic Dark States in Single-layer Tungsten Disulfide
• Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides
• Magnetic Control of Valley Pseudospin in Monolayer WSe2
• Valley Zeeman Effect in Elementary Optical Excitations of a Monolayer WSe2
• Breaking of valley degeneracy by magnetic field in monolayer MoSe2
• Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides
• Valley Splitting and Polarization by the Zeeman Effect in Monolayer MoSe2
• Robust optical emission polarization in MoS2 monolayers through selective valley excitation
• Tight-binding model and direct-gap/indirect-gap transition in single-layer and multi-layer MoS${}_2$
• Exciton Diamagnetic Shifts and Valley Zeeman Effects in Monolayer WS${}_2$ and MoS${}_2$ to 65 Tesla
• Band nesting and the optical response of two-dimensional semiconducting transition metal dichalcogenides
• Exciton band structure of monolayer MoS2
• WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature
• Effective lattice Hamiltonian for monolayer MoS2 : Tailoring electronic structure with perpendicular electric and magnetic fields
• \textit{Ab-initio} Tight-Binding Hamiltonian for Transition Metal Dichalcogenides
• Exciton band structure in layered MoSe2: from a monolayer to the bulk limit
• Optical manipulation of the exciton charge state in single layer tungsten disulfide
• Electron interactions in graphene in a strong magnetic field
• Valley-spin polarized Landau levels in a monolayer semiconductor
• Control of Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers
• Polarization and time-resolved photoluminescence spectroscopy of excitons in MoSe2 monolayers
• Magnetic control of the valley degree of freedom of massive Dirac fermions with application to transition metal dichalcogenides
• Magneto-optics in transition metal diselenide monolayers
• Excitonic valley effects in monolayer WS${}_2$ under high magnetic fields
• A tight-binding model for MoS${}_2$ monolayers
• Magneto-excitons in large area CVD grown monolayer MoS${}_2$ and MoSe${}_2$ on sapphire
• Electronic Band Structure of Transition Metal Dichalcogenides from Ab Initio and Slater-Koster Tight-Binding Model
• A Tight Binding Approach to Strain and Curvature in Monolayer Transition-Metal Dichalcogenides
• Atomically inspired $k\cdot p$ approach and valley Zeeman effect in transition metal dichalcogenide monolayers
• Landau levels and Shubnikov-de Haas oscillations in monolayer transition metal dichalcogenide semiconductors

Cited by in corpus (13)

• Ab-initio studies of exciton $g$ factors: Monolayer transition metal dichalcogenides in magnetic fields
• Valley Zeeman effect and Landau levels in Two-Dimensional Transition Metal Dichalcogenides
• Probing exciton dispersions of freestanding monolayer WSe2 by momentum resolved electron energy loss spectroscopy
• Tutorial: Exciton resonances for atomically-thin optics
• Gate controlled quantum dots in monolayer WSe2
• Band nesting and exciton spectrum in monolayer MoS${}_2$
• Valley two-qubit system in a MoS${}_2$-monolayer gated double quantum dot
• The effect of valley, spin and band nesting on the electronic properties of gated quantum dots in a single layer of transition metal dichalcogenides (TMDCs)
• Excitonic Absorption Signatures of Twisted Bilayer WSe${}_2$ by Electron Energy-Loss Spectroscopy
• Comparative Analysis of Tight-Binding models for Transition Metal Dichalcogenides
• Interacting holes in a gated WSe${}_2$ quantum channel: valley correlations and zigzag Wigner crystal
• Electrically tunable MoSe${}_2$/WSe${}_2$ heterostructure-based quantum dot
• Spin-valley qubits in gated quantum dots in a single layer of transition metal dichalcogenides