Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides

Abstract

We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides $M{X}_2$ ($M$=Mo, W; $X$=S, Se, Te). As the conduction and valence band edges are predominantly contributed by the $d_{z^2}$, $d_{xy}$, and $d_{x^2-y^2}$ orbitals of $M$ atoms, the TB model is constructed using these three orbitals based on the symmetries of the monolayers. Parameters of the TB model are fitted from the first-principles energy bands for all $M{X}_2$ monolayers. The TB model involving only the nearest-neighbor $M$-$M$ hoppings is sufficient to capture the band-edge properties in the $\pm K$ valleys, including the energy dispersions as well as the Berry curvatures. The TB model involving up to the third-nearest-neighbor $M$-$M$ hoppings can well reproduce the energy bands in the entire Brillouin zone. Spin-orbit coupling in valence bands is well accounted for by including the on-site spin-orbit interactions of $M$ atoms. The conduction band also exhibits a small valley-dependent spin splitting which has an overall sign difference between Mo$X_2$ and W$X_2$. We discuss the origins of these corrections to the three-band model. The three-band TB model developed here is efficient to account for low-energy physics in $M{X}_2$ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.

11 pages, 10 figures, 4 tables

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Cited by in corpus (431)

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• Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe${}_2$
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• Temperature Dependent Valley Relaxation Dynamics in Single Layer WS2 Measured Using Ultrafast Spectroscopy
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• Optical generation and detection of pure valley current in monolayer transition metal dichalcogenides
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• Orbital Hall physics in two-dimensional Dirac materials
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• Lateral Interfaces of Transition Metal Dichalcogenides: A Stable Tunable One-Dimensional Physics Platform
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• Optical selection rules for excitonic Rydberg series in the massive Dirac cones of hexagonal 2D materials
• Large spin-to-charge conversion at the two-dimensional interface of transition metal dichalcogenides and permalloy
• Exciton-Trion-Polaritons in Two-Dimensional Materials
• Energy-resolved Photoconductivity Mapping in a Monolayer-bilayer WSe2 Lateral Heterostructure
• Magneto-optical Kerr effect in spin split two-dimensional massive Dirac materials
• Spin-valley system in a gated MoS${}_2$-monolayer quantum dot
• Strong Valley Zeeman Effect of Dark Excitons in Monolayer Transition Metal Dichalcogenides in a Tilted Magnetic Field
• Single-electron Transport in Graphene-like Nanostructures
• Ab initio phonon self-energies and fluctuation diagnostics of phonon anomalies: Lattice instabilities from Dirac pseudospin physics in transition metal dichalcogenides
• Assessing the role of interatomic position matrix elements in tight-binding calculations of optical properties
• Sliding Ferroelectrics Induced Hybrid-Order Topological Phase Transitions
• Quasiparticle energy bands and Fermi surfaces of monolayer NbSe${}_2$
• Electronic Structure of Exfoliated Millimeter-Sized Monolayer WSe2 on Silicon Wafer
• Strain control of exciton and trion spin-valley dynamics in monolayer transition metal dichalcogenides
• Valley Degree of Freedom in Two-Dimensional van der Waals Materials
• Symmetry and Control of Spin-Scattering Processes in Two-Dimensional Transition Metal Dichalcogenides
• Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides
• Orbital Fulde-Ferrell pairing state in moiré Ising superconductors
• Hidden Breathing Kagome Topology in Hexagonal Transition Metal Dichalcogenides
• Magnetic field dependence of electronic properties of MoS${}_2$ quantum dots with different edges
• Possible charge-density-wave signatures in the anomalous resistivity of Li-intercalated multilayer MoS2
• Electronic and Optical properties of transition metal dichalcogenides under symmetric and asymmetric field-effect doping
• Landau Levels in 2D materials using Wannier Hamiltonians obtained by first principles
• Topological phases and twisting of graphene on a dichalcogenide monolayer
• Nonpolar m-plane GaN/AlGaN heterostructures with intersubband transitions in the 5 to 10 THz band
• Valley two-qubit system in a MoS${}_2$-monolayer gated double quantum dot
• Voltage-controlled long-range propagation of indirect excitons in van der Waals heterostructure
• Unconventional superconductivity and anomalous response in hole-doped transition metal dichalcogenides
• Spin accumulation and dynamics in inversion-symmetric van der Waals crystals
• Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
• Proximity-induced topological phases in bilayer graphene
• One-dimensional topological superconductivity based entirely on phase control
• Spin-dependent Refraction at the Atomic Step of Transition-metal Dichalcogenides
• Charged exctions in two-dimensional transition-metal dichalcogenides - semiclassical calculation of Berry-curvature effects
• Optically bright $p$-excitons indicating strong Coulomb coupling in transition-metal dichalcogenides
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• Role of Interlayer Coupling in the Second Harmonic Generation of Bilayer Transition-metal Dichalcogenides
• Exciton routing in the heterostructure of TMD and paraelectrics
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• Valley polarized magnetic state in hole-doped mono layers of transition metal dichalcogenides
• In-Plane Electric Field Induced Orbital Hybridization of Excitonic States In Monolayer WSe2
• Exploration of the bright and dark exciton landscape and fine structure of MoS${}_2$ (using G${}_0$W${}_0$-BSE)
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• Intervalley electron-hole exchange interaction and impurity-assisted recombination of indirect excitons in WS${}_2$ and WSe${}_2$ monolayers
• Proximity-Induced Mixed Odd and Even Frequency Pairings in Monolayer NbSe${}_2$
• Magneto photoluminescence measurements of tungsten disulphide monolayers
• An efficient method for hybrid density functional calculation with spin-orbit coupling
• Large g factor in bilayer WS${}_2$ flakes
• $\Gamma$-valley assisted intervalley scattering on monolayer and bilayer WS2 revealed by time-resolved Kerr rotation spectroscopy
• Twisted Bogoliubov quasiparticles in the superconducting NbSe${}_2$ monolayer on graphene
• Strongly enlarged topological regime and enhanced superconducting gap in nanowires coupled to Ising superconductors
• Long range of indirect exchange interaction on the edges of MoS${}_2$ flakes
• Spin relaxation in hole-doped transition metal dichalcogenide monolayer and bilayer with the crystal defects
• Triangular lattice exciton model
• Quantum-Geometric Origin of Out-of-plane Stacking Ferroelectricity
• Exciton solid in bilayer two dimensional electron-hole systems
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• Subcycle control of valley-selective excitation via dynamical Franz-Keldysh effect in WSe${}_2$ monolayer
• Interplay of valley polarized dark trion and dark exciton-polaron in monolayer WSe2
• Nonclassical Light from Exciton Interactions in a Two-Dimensional Quantum Mirror
• Detecting the spread of valence band Wannier functions by optical sum rules
• Symmetry manipulation of nonlinear optical effect for metallic TMDC
• Disorder-induced coupling of Weyl nodes in WTe${}_2$
• Spin-orbit-stable type-II nodal line band crossing in n-doped monolayer MoX2 (X=S,Se,Te)
• Entropy per particle spikes in the transition metal dichalcogenides
• Orbital-dependent quasiparticle scattering interference in 3R-NbS2
• Signature of Orbital Driven Finite Momentum Pairing in a 3D Ising Superconductor
• Electrical valley filtering in transition metal dichalcogenides
• Gate-controlled supercurrent reversal in MoS${}_2$-based Josephson junctions
• Spin triplet superconducting pairing in doped MoS${}_2$
• Reversible edge spin currents in antiferromagnetically proximitized dichalcogenides
• Third-order Optical Nonlinearity in Two-dimensional Transition Metal Dichalcogenides
• Magnetic field mixing and splitting of bright and dark excitons in monolayer MoSe2
• Entropy Signatures of Topological Phase Transitions
• Unraveling the unusually high electrical conductivity of the delafossite metal PdCoO${}_2$
• Probing the order parameter symmetry of two-dimensional superconductors by twisted Josephson interferometry
• Magneto-reflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields
• Time-reversal symmetry breaking superconductivity in hole-doped monolayer MoS${}_2$
• High-field Studies on Layered Magnetic and Polar Dirac Metals
• Coulomb effects in the absorbance spectra of two-dimensional Dirac materials
• Effective Dynamics of 2D Bloch Electrons in External Fields Derived From Symmetry
• Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors
• Geometric band properties in strained monolayer transition metal dichalcogenides using simple band structures
• Ab-initio calculations for electronic and optical properties of Er${}_{\mathrm{W}}$ defects in tungsten disulfide
• Effect of intravalley and intervalley electron-hole exchange on the nonlinear optical response of monolayer MoSe${}_2$
• Advancing excited-state properties of two-dimensional materials using a dielectric-dependent hybrid functional
• Proximity-induced spin-polarized magnetocaloric effect in transition metal dichalcogenides
• Inducing chiral superconductivity on honeycomb lattice systems
• Spin Response and Collective Modes in Simple Metal Dichalcogenides
• Electrical control of orbital and vibrational interlayer coupling in bi- and trilayer 2H-MoS${}_2$
• Magnetization amplification in the interlayer pairing superconductor 4Hb-TaS${}_2$
• Large photoluminescence enhancement by an out-of-plane magnetic field in exfoliated WS${}_2$ flakes
• Proximity-induced topological transition and strain-induced charge transfer in graphene/MoS2 bilayer heterostructures
• Optical Switching of Moiré Chern Ferromagnet
• Nonlinear optical Hall effect of few-layered NbSe2
• Pressure-tuned many-body phases through $\Gamma$-K valleytronics in moiré bilayer WSe${}_2$
• Effect of one-dimensional superlattice potentials on the band gap of two-dimensional materials
• Metal-insulator transitions in bilayer electron-hole systems in transition metal dicalcogenides
• Magneto-optical conductivity of monolayer transition metal dichalcogenides in the presence of proximity-induced exchange interaction and external electrical field
• Electron dynamics in a 2D nanobubble: A two-level system based on spatial density
• Femtosecond currents in transition metal dichalcogenides monolayers
• Stable $2R$ van der Waals heterostructures of NbS${}_2$ and $M$Se${}_2$ for $M$=Mo and W
• Friedel oscillations and chiral superconductivity in monolayer NbSe${}_2$
• Valley-resolved Fano resonance in monolayer transition metal dichalcogenides nanoribbons with attached stubs
• Choosing Tight-Binding Models for Accurate Optoelectronic Responses
• Robust one-dimensionality at twin-grain-boundaries in MoSe${}_2$
• Tunneling in an anisotropic cubic Dirac semi-metal
• Photocurrent of exciton polaritons
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Dependence of the magnetic interactions in MoS${}_2$ monolayer on Mn-doping configurations
• Valley polarization and valleyresistance in monolayer transition metal dichalcogenides superlattice
• Topological Interlayer Superconductivity in a van der Waals Heterostructure
• Two-Dimensional Multifunctional Materials from Endohedral Fullerenes
• Orbital Hall effect and topology on a two-dimensional triangular lattice: from bulk to edge
• Coulomb effects on topological band inversion in the moiré of WSe${}_2$/BAs heterobilayer
• Topologically protected flatness in chiral moiré heterostructures
• Unconventional pairing in Ising superconductors: Application to monolayer NbSe${}_2$
• Mixed quantum-classical modeling of exciton-phonon scattering in solids: Application to optical linewidths of monolayer MoS2
• Hydrogenic Spin-Valley states of the Bromine donor in 2H-MoTe${}_2$
• Effective lattice Hamiltonian for monolayer tin disulphide: tailoring electronic structure with electric and magnetic fields
• Valley spin-acoustic resonance in MoS${}_2$ monolayers
• Engineering chiral topological superconductivity in twisted Ising superconductors
• Band structure of molybdenum disulfide: from first principle to analytical band model
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Quantum Oscillation in Excitonic Insulating Electron-Hole Bilayer
• Magneto-Optical Measurements of the Negatively Charged 2$s$ Exciton in WSe${}_2$
• Magnetizations and de Haas-van Alphen oscillations in massive Dirac fermions
• Switchable valley functionalities of an $n-n^{-}-n$ junction in 2D semiconductors
• Optically and electrically controllable adatom spin-orbital dynamics in transition metal dichalcogenides
• Comparative Analysis of Tight-Binding models for Transition Metal Dichalcogenides
• Spin susceptibility in interacting two-dimensional semiconductors and bilayer systems at first order: Kohn anomalies and spin density wave ordering
• Magnetic phase transitions in two-dimensional two-valley semiconductors with in-plane magnetic field
• Nonreciprocal phonon dichroism induced by Fermi pocket anisotropy in two-dimensional Dirac materials
• Topological transitions in two-dimensional Floquet superconductors
• Dichotomy of saddle points in energy bands of a monolayer NbSe${}_2$
• Optically induced spin Hall current in Janus transition-metal dichalcogenides
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Spin Pumping into two-dimensional systems
• Wannier-Function-Based Approach to Coupled Exciton-Phonon-Photon Dynamics in Two-Dimensional Semiconductors
• The stabilizer group of honeycomb lattices and its application to deformed monolayers
• Robustness of momentum-indirect interlayer excitons in MoS2/WSe2 heterostructure against charge carrier doping
• Topological Kondo semimetals emulated in hetero-bilayer transition metal dichalcogenides
• Dissecting intervalley coupling mechanisms in monolayer transition metal dichalcogenides
• Quantum Hall ferromagnets and transport properties of buckled Dirac materials
• Theory of field-modulated spin-valley-orbital pseudospin physics
• Optical injection of a spin current into a zigzag nanoribbon of monolayer MoS2 with antiferromagnetic Kekule distortion
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Pump-driven opto-magnetic properties in semiconducting transition-metal dichalcogenides: an analytical model
• Flat Band Generation through Interlayer Geometric Frustration in Intercalated Transition Metal Dichalcogenides
• Symmetry-dependent antiferromagnetic proximity effects on valley splitting
• High magnetic field spin-valley-split Shubnikov-de Haas oscillations in a WSe${}_2$ monolayer
• Longitudinal and transverse mobilities of $n$-type monolayer transition metal dichalcogenides in the presence of proximity-induced interactions at low temperature
• Construction of optimized tight-binding models using \textit{ab initio} Hamiltonian: Application to monolayer $2H$-transition metal dichalcogenides
• Spin relaxation and the Kondo effect in transition metal dichalcogenide monolayers
• Optically tunable spin Hall effect in periodically driven monolayer transition metal dichalcogenides
• Three-orbital continuous model for $1H$-type metallic transition-metal dichalcogenide monolayers
• Complete Spin and Valley Polarization by Total External Reflection from Potential Barriers in Bilayer Graphene and Monolayer Transition Metal Dichalcogenides
• Berry curvature and quantum metric in copper-substituted lead phosphate apatite
• Electrically tunable MoSe${}_2$/WSe${}_2$ heterostructure-based quantum dot
• Effective K valley Hamiltonian for TMD bilayers under pressure and application to twisted bilayers with pressure-induced topological phase transitions
• Microscopic Theory of Exciton-Exciton Annihilation in Two-Dimensional Semiconductors
• A Practical Introduction to Density Functional Theory
• Spin polarization in Lateral two-dimensional Heterostructures
• Dynamical Orbital Angular Momentum Induced by Circularly Polarized Phonons
• Positivity Preserving Density Matrix Minimization at Finite Temperatures via Square Root
• Plasmonic detection of Rashba spin-orbit coupling in monolayer transition-metal dichalcogenides
• Absorbance marker: Detection of quantum geometry and spread of Wannier function in disordered 2D semiconductors
• Excitation energy dependence of Raman spectra of few-layer WS2
• Observation of the Interlayer Exciton Gases in WSe${}_2$ -p: WSe${}_2$ Heterostructures
• Phase-matching-free parametric oscillators based on two dimensional semiconductors
• Quantum oscillations of valley current driven by microwave irradiation in transition-metal dichalcogenide/ferromagnet hybrids
• Comparison of band-fitting and Wannier-based model construction for WSe${}_2$
• Spin-valley qubits in gated quantum dots in a single layer of transition metal dichalcogenides
• Quantization Phenomena of critical Hamiltonians in 2D systems
• Three-level Spaser System: a Semi-Classical Analysis
• Deciphering the Intense Post-Gap Absorptions of Monolayer Transition Metal Dichalcogenides
• Robust Interlayer Exciton Interplay in Twisted van der Waals Heterotrilayer on a Broadband Bragg Reflector up to Room Temperature
• Yu-Shiba-Rusinov States in Ising Superconductors
• Spin and valley filter based on two-dimensional WSe${}_2$ heterostructures
• Unconventional bright ground-state excitons in monolayer TiI${}_2$ from first-principles calculations