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

We theoretically investigate the electronic states in monolayer NbSe$_2$ and develop continuous models to describe these states in Fermi pockets. In $1H$-type metallic transition-metal dichalcogenides(TMDCs), the Femi surface consists of three pockets enclosing the $\Gamma$, $K$, and $K'$ points. We reveal that the conventional effective model used for semiconducting TMDCs is not sufficient to describe the electronic states in metallic TMDCs and thus introduce a scheme to construct the effective model from the first-principles results. All models can be represented by $3\times3$ Hamiltonian and well reproduce electronic states around the Fermi energy in terms of the orbital composition and the phase factor. We also show that the $p$ orbitals in chalcogen atoms, which are ignored in the conventional $2\times2$ model, play a crucial role in metallic TMDCs. Although the aim of these models is to reproduce electronic states, they can well describe states near the high-symmetry points and the profile of Berry curvature in the wave vector space. The continuous model can be a handleable tool to describe the electronic states and to analyze the transport phenomena in metallic TMDCs.