Atomically inspired $k\cdot p$ approach and valley Zeeman effect in transition metal dichalcogenide monolayers

Abstract

We developed a six-band $k\cdot p$ model that describes the electronic states of monolayer transition metal dichalcogenides (TMDCs) in $K$-valleys. The set of parameters for the $k\cdot p$ model is uniquely determined by decomposing tight-binding (TB) models in the vicinity of $K^{\pm }$-points. First, we used TB models existing in literature to derive systematic parametrizations for different materials, including MoS${}_2$, WS${}_2$, MoSe${}_2$ and WSe${}_2$. Then, by using the derived six-band $k\cdot p$ Hamiltonian we calculated effective masses, Landau levels, and the effective exciton $g$-factor $g_{X^0}$ in different TMDCs. We showed that TB parameterizations existing in literature result in small absolute values of $g_{X^0}$, which are far from the experimentally measured $g_{X^0}\approx -4$. To further investigate this issue we derived two additional sets of $k\cdot p$ parameters by developing our own TB parameterizations based on simultaneous fitting of ab-initio calculated, within the density functional (DFT) and $GW$ approaches, energy dispersion and the value of $g_{X^0}$. We showed that the change in TB parameters, which only slightly affects the dispersion of higher conduction and deep valence bands, may result in a significant increase of $|g_{X^0}|$, yielding close-to-experiment values of $g_{X^0}$. Such a high parameter sensitivity of $g_{X^0}$ opens a way to further improvement of DFT and TB models.

9 pages, 4 figures, 5 tables

References in corpus (20)

• Tightly bound excitons in monolayer WSe2
• k.p theory for two-dimensional transition metal dichalcogenide semiconductors
• Magnetic Control of Valley Pseudospin in Monolayer WSe2
• Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2
• Valley Zeeman Effect in Elementary Optical Excitations of a Monolayer WSe2
• Breaking of valley degeneracy by magnetic field in monolayer MoSe2
• Valley Splitting and Polarization by the Zeeman Effect in Monolayer MoSe2
• Robust optical emission polarization in MoS2 monolayers through selective valley excitation
• Exciton Diamagnetic Shifts and Valley Zeeman Effects in Monolayer WS${}_2$ and MoS${}_2$ to 65 Tesla
• Vibrational and optical properties of MoS${}_2$: from monolayer to bulk
• \textit{Ab-initio} Tight-Binding Hamiltonian for Transition Metal Dichalcogenides
• Theory of strain in single-layer transition metal dichalcogenides
• Magneto-optics in transition metal diselenide monolayers
• Spin and valley dynamics of excitons in transition metal dichalcogenides monolayers
• Optical investigation of monolayer and bulk tungsten diselenide (WSe${}_2$) in high magnetic fields
• Discrete quantum dot like emitters in monolayer MoSe2: Spatial mapping, Magneto-optics and Charge tuning
• A tight-binding model for MoS${}_2$ monolayers
• Valley Zeeman effect and spin-valley polarized conductance in monolayer MoS${}_2$ in a perpendicular magnetic field
• Magneto-excitons in large area CVD grown monolayer MoS${}_2$ and MoSe${}_2$ on sapphire
• Landau levels and Shubnikov-de Haas oscillations in monolayer transition metal dichalcogenide semiconductors

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• Giant paramagnetism induced valley polarization of electrons in charge-tunable monolayer MoSe2
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• Zeeman Splitting and Inverted Polarization of Biexciton Emission in Monolayer WS2
• Giant Valley-Zeeman Splitting from Spin-Singlet and Spin-Triplet Interlayer Excitons in WSe2/MoSe2 Heterostructure
• Direct Observation of Gate Tunable Dark Trions in Monolayer WSe2
• Ab-initio studies of exciton $g$ factors: Monolayer transition metal dichalcogenides in magnetic fields
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• Measurement of Conduction and Valence Bands g-factors in a Transition Metal Dichalcogenide Monolayer
• Valley Zeeman effect and Landau levels in Two-Dimensional Transition Metal Dichalcogenides
• Electrically controlled emission from singlet and triplet exciton species in atomically thin light emitting diodes
• Band nesting, massive Dirac Fermions and Valley Lande and Zeeman effects in transition metal dichalcogenides: a tight-binding model
• Dark exciton-exciton annihilation in monolayer WSe${}_2$
• Monolayer transition metal dichalcogenides in strong magnetic fields: Validating the Wannier model using a microscopic calculation
• Magnetoexcitons in transition-metal dichalcogenides monolayers, bilayers, and van der Waals heterostructures
• Effects of parallel electric and magnetic fields on Rydberg excitons in buckled two-dimensional materials
• High harmonic generation in monolayer MoS2 controlled by resonant and near-resonant pulses on ultrashort time scales
• Large g factor in bilayer WS${}_2$ flakes
• DFT2kp: effective kp models from ab-initio data
• Geometric band properties in strained monolayer transition metal dichalcogenides using simple band structures
• Magnetic field control of light-induced spin accumulation in monolayer MoSe${}_2$
• Coherent spin dynamics of excitons in strained monolayer semiconductors
• Large photoluminescence enhancement by an out-of-plane magnetic field in exfoliated WS${}_2$ flakes
• Excitons in Atomically Thin TMD in Electric and Magnetic Fields
• Hyperfine interaction in atomically thin transition metal dichalcogenides