Effective lattice Hamiltonian for monolayer MoS<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>2</mml:mn></mml:msub></mml:math>: Tailoring electronic structure with perpendicular electric and magnetic fields

Rostami, Habib; Moghaddam, Ali G.; Asgari, Reza

doi:10.1103/physrevb.88.085440

Cited by 225 publications

(259 citation statements)

References 41 publications

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“…Thus far, only two types of approaches have been considered toward this goal: i) oversimplified models such as k · p theory and tight-binding hamiltonians with few bands involving only the d orbitals of the metal atoms 13,[23][24][25] ; ii) fitted models that contain all the details of the ab-initio calculations, often parametrized as a tight-binding hamiltonian with a large number of parameters fitted to reproduce the ab-initio results 26,27 . While both types of approaches are valuable and interesting, they each have certain deficiencies: In the first type of approach, the physics is transparent due to the small number of basis functions and parameters involved, but not necessarily accurate or reliable.…”

Section: Introductionmentioning

confidence: 99%

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

et al. 2015

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We present an accurate ab-initio tight-binding hamiltonian for the transition-metal dichalcogenides, MoS2, MoSe2, WS2, WSe2, with a minimal basis (the d orbitals for the metal atoms and p orbitals for the chalcogen atoms) based on a transformation of the Kohn-Sham density function theory (DFT) hamiltonian to a basis of maximally localized Wannier functions (MLWF). The truncated tight-binding hamiltonian (TBH), with only on-site, first and partial second neighbor interactions, including spin-orbit coupling, provides a simple physical picture and the symmetry of the main band-structure features. Interlayer interactions between adjacent layers are modeled by transferable hopping terms between the chalcogen p orbitals. The full-range tight-binding hamiltonian (FTBH) can be reduced to hybrid-orbital k · p effective hamiltonians near the band extrema that captures important low-energy excitations. These ab-initio hamiltonians can serve as the starting point for applications to interacting many-body physics including optical transitions and Berry curvature of bands, of which we give some examples.

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Section: Introductionmentioning

confidence: 99%

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

et al. 2015

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“…After the two-band k · p model describing the conduction and valence bands around the two valleys (K and K ′ points) in the hexagonal Brillouin zone of LTMD 27 , several TB models in various approximations have been proposed to reproduce the first-principles band structure of pristine LTMD 23,[28][29][30][31] . Among them, the TB model of Zahid et al 29 , including nonorthogonal sp 3 d 5 orbitals of M and X atoms and spin-orbit coupling, is able to accurately reproduce the first-principles bands for a wide range of energies in the Brillouin zone.…”

Section: Introductionmentioning

confidence: 99%

Atomic defect states in monolayers of MoS2 and WS2

Salehi

Saffarzadeh

2016

Surface Science

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The influence of atomic vacancy defects at different concentrations on electronic properties of MoS 2 and WS 2 monolayers is studied by means of Slater-Koster tight-binding model with non-orthogonal sp 3 d 5 orbitals and including the spin-orbit coupling. The presence of vacancy defects induces localized states in the bandgap of pristine MoS 2 and WS 2 , which have potential to modify the electronic structure of the systems, depending on the type and concentration of the defects. It is shown that although the contribution of metal (Mo or W) d orbitals is dominant in the formation of midgap states, the sulphur p and d orbitals have also considerable contribution in the localized states, when metal defects are introduced. Our results suggest that Mo and W defects can turn the monolayers into p-type semiconductors, while the sulphur defects make the system a n-type semiconductor, in agreement with ab initio results and experimental observations.

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“…2d [27][28][29][30] . For independent electron-hole pair excitations with a vanishing in-plane momentum, the optical transition in each valley experiences a shift in energy which is linear in B, given by…”

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Valley Zeeman effect in elementary optical excitations of monolayer WSe2

et al. 2015

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A monolayer of a transition metal dichalcogenide such as WSe 2 is a two-dimensional direct-bandgap valley-semiconductor 1,2 having an e ective honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly polarized light fields 3-5 , suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom 6-8 . Here we report such experiments that demonstrate the valley Zeeman e ect-strongly anisotropic lifting of the degeneracy of the valley pseudospin degree of freedom using an external magnetic field. The valley-splitting measured using the exciton transition deviates appreciably from values calculated using a three-band tight-binding model 9 for an independent electron-hole pair at ±K valleys. We show, on the other hand, that a theoretical model taking into account the strongly bound nature of the exciton yields an excellent agreement with the experimentally observed splitting. In contrast to the exciton, the trion transition exhibits an unexpectedly large valley Zeeman e ect that cannot be understood within the same framework, hinting at a di erent contribution to the trion magnetic moment. Our results raise the possibility of controlling the valley degree of freedom using magnetic fields in monolayer transition metal dichalcogenides or observing topological states of photons strongly coupled to elementary optical excitations in a microcavity 10 .Charge carriers in two-dimensional (2D) layered materials with a honeycomb lattice, such as graphene and transition metal dichalcogenides (TMDs), have a twofold valley degree of freedom labelled by ±K-points of the Brillouin zone, which are related to each other by time-reversal symmetry 7 . In TMDs, the low-energy physics takes place in the vicinity of ±K-points of the conduction and valence bands with Bloch states that are formed primarily from d z 2 and d x 2 −y 2 , d xy orbitals of the transition metal, respectively 9 . The magnetic moment of charged particles in a monolayer TMD arises from two distinct contributions: the intracellular component stems from the hybridization of the d x 2 −y 2 and d xy orbitals as d x 2 −y 2 ± id xy , which provide the Bloch electrons at ±K in the valence band an azimuthal angular momentum along z of l z = ±2h (Fig. 1a). The second-intercellular-contribution originates from the phase winding of the Bloch functions at ±K-points 11-14 . This latter contribution to orbital magnetic moment is different for conduction and valence bands owing to breakdown of electronhole symmetry. Both contributions yield magnetic-field-induced splitting with an opposite sign in the two valleys.In a 2D material such as a monolayer TMD, the current circulation from the orbitals can only be within the plane; as a consequence, the corresponding orbital magnetic moment can only point out-of-plane. A magnetic field (B) along z distinguishes the sense of circulation in 2D, causing opposite energy shifts (− µ· B) in ±K val...

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Effective lattice Hamiltonian for monolayer MoS2: Tailoring electronic structure with perpendicular electric and magnetic fields

Cited by 225 publications

References 41 publications

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

Atomic defect states in monolayers of MoS2 and WS2

Valley Zeeman effect in elementary optical excitations of monolayer WSe2

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