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We theoretically investigate the electronic states in monolayer NbSe$_2$ anddevelop continuous models to describe these states in Fermi pockets. In$1H$-type metallic transition-metal dichalcogenides(TMDCs), the Femi surfaceconsists of three pockets enclosing the $\Gamma$, $K$, and $K'$ points. Wereveal that the conventional effective model used for semiconducting TMDCs isnot sufficient to describe the electronic states in metallic TMDCs and thusintroduce a scheme to construct the effective model from the first-principlesresults. All models can be represented by $3\times3$ Hamiltonian and wellreproduce electronic states around the Fermi energy in terms of the orbitalcomposition and the phase factor. We also show that the $p$ orbitals inchalcogen atoms, which are ignored in the conventional $2\times2$ model, play acrucial role in metallic TMDCs. Although the aim of these models is toreproduce electronic states, they can well describe states near thehigh-symmetry points and the profile of Berry curvature in the wave vectorspace. The continuous model can be a handleable tool to describe the electronicstates and to analyze the transport phenomena in metallic TMDCs.

Three-orbital continuous model for $1H$-type metallic transition-metal dichalcogenide monolayers