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Register a new userBand nesting, massive Dirac Fermions and Valley Lande and Zeeman effects in transition metal dichalcogenides: a tight-binding model
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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.
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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.
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.
This paper presents a theoretical description of both the valley Zeeman effect (g-factors) and Landau levels in two-dimensional H-phase transition metal dichalcogenides (TMDs) using the Luttinger-Kohn approximation with spin-orbit coupling. At the valley extrema in TMDs, energy bands split into Landau levels with a Zeeman shift in the presence of a uniform out-of-plane external magnetic field. The Landau level indices are symmetric in the $K$ and $K$ valleys. We develop a numerical approach to compute the single band g-factors from first principles without the need for a sum over unoccupied bands. Many-body effects are included perturbatively within the GW approximation. Non-local exchange and correlation self-energy effects in the GW calculations increase the magnitude of single band g-factors compared to those obtained from density functional theory. Our first principles results give spin- and valley-split Landau levels, in agreement with recent optical experiments. The exciton g-factors deduced in this work are also in good agreement with experiment for the bright and dark excitons in monolayer WSe$_2$, as well as the lowest-energy bright excitons in MoSe$_2$-WSe$_2$ heterobilayers with different twist angles.
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.
The kagome lattice is a two-dimensional network of corner-sharing triangles known as a platform for exotic quantum magnetic states. Theoretical work has predicted that the kagome lattice may also host Dirac electronic states that could lead to topological and Chern insulating phases, but these have evaded experimental detection to date. Here we study the d-electron kagome metal Fe$_3$Sn$_2$ designed to support bulk massive Dirac fermions in the presence of ferromagnetic order. We observe a temperature independent intrinsic anomalous Hall conductivity persisting above room temperature suggestive of prominent Berry curvature from the time-reversal breaking electronic bands of the kagome plane. Using angle-resolved photoemission, we discover a pair of quasi-2D Dirac cones near the Fermi level with a 30 meV mass gap that accounts for the Berry curvature-induced Hall conductivity. We show this behavior is a consequence of the underlying symmetry properties of the bilayer kagome lattice in the ferromagnetic state with atomic spin-orbit coupling. This report provides the first evidence for a ferromagnetic kagome metal and an example of emergent topological electronic properties in a correlated electron system. This offers insight into recent discoveries of exotic electronic behavior in kagome lattice antiferromagnets and may provide a stepping stone toward lattice model realizations of fractional topological quantum states.
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