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Register a new userRealistic tight-binding model for monolayer transition metal dichalcogenides in 1T structure
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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. For a better understanding of their properties, in particular their responses to external fields, we construct a realistic four-band tight-binding (TB) model by combining the symmetry analysis and first-principles calculations. Our TB model respects all the symmetries and can accurately reproduce the band structure in a large energy window from -0.3 eV to 0.8 eV. With the inclusion of spin-orbital coupling (SOC), our TB model can characterize the nontrivial topology and the corresponding edge states. Our TB model can also capture the anisotropic strain effects on the band structure and the strain-induced metal-insulator transition. Moreover, we found that although $MX_2$ share the same crystal structures and have the same crystal symmetries, while the orbital composition of states around the Fermi level are qualitatively different and their lower-energy properties cannot fully described by a single k $cdot$ p model. Thus, we construct two different types of k $cdot$ p model for $M$S$_2$,$M$Se$_2$ and $M$Te$_2$, respectively. Benefiting from the high accuracy and simplicity, our TB and k $cdot$ p models can serve as a solid and concrete starting point for future studies of transport, superconductivity, strong correlation effects and twistronics in 1T-transition metal dichalcogenides.
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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 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 $MX_2$ 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 $MX_2$ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.
The optical properties of atomically thin transition metal dichalcogenide (TMDC) semiconductors are shaped by the emergence of correlated many-body complexes due to strong Coulomb interaction. Exceptional electron-hole exchange predestines TMDCs to study fundamental and applied properties of Coulomb complexes such as valley depolarization of excitons and fine-structure splitting of trions. Biexcitons in these materials are less understood and it has been established only recently that they are spectrally located between exciton and trion. Here we show that biexcitons in monolayer TMDCs exhibit a distinct fine structure on the order of meV due to electron-hole exchange. Ultrafast pump-probe experiments on monolayer WSe$_2$ reveal decisive biexciton signatures and a fine structure in excellent agreement with a microscopic theory. We provide a pathway to access biexciton spectra with unprecedented accuracy, which is valuable beyond the class of TMDCs, and to understand even higher Coulomb complexes under the influence of electron-hole exchange.
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 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 textit{p} orbitals. The full-range tight-binding hamiltonian (FTBH) can be reduced to hybrid-orbital k $cdot$ p effective hamiltonians near the band extrema that captures important low-energy excitations. These textit{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.
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.
Monolayer transition-metal dichalcogenides are direct gap semiconductors with great promise for optoelectronic devices. Although spatial correlation of electrons and holes plays a key role, there is little experimental information on such fundamental properties as exciton binding energies and band gaps. We report here an experimental determination of exciton excited states and binding energies for monolayer WS2 and WSe2. We observe peaks in the optical reflectivity/absorption spectra corresponding to the ground- and excited-state excitons (1s and 2s states). From these features, we determine lower bounds free of any model assumptions for the exciton binding energies as E2sA - E1sA of 0.83 eV and 0.79 eV for WS2 and WSe2, respectively, and for the corresponding band gaps Eg >= E2sA of 2.90 and 2.53 eV at 4K. Because the binding energies are large, the true band gap is substantially higher than the dominant spectral feature commonly observed with photoluminescence. This information is critical for emerging applications, and provides new insight into these novel monolayer semiconductors.
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