We revisit the electronic structure and band topology of monolayer ${1\mathrm{H}-\mathrm{NbSe}}_2$ and its related compounds ${1\mathrm{H}-\mathrm{MoS}}_2$, ${\mathrm{NbS}}_2$, ${\mathrm{TaS}}_2$, ${\mathrm{TaSe}}_2$, and ${\mathrm{WS}}_2$. We construct a six-band, a three-band, and—simplest of all—a single-band model for this material family, by directly Wannierizing the ab initio bands. All hosts obstructed atomic isolated bands away from the atomic positions near the Fermi energy. We find that in the three-band model, the obstructed atomic Wannier function can be well approximated by an optimally compact Wannier function with more than 90% accuracy for all the compounds, rising to a remarkable 94% accuracy in ${\mathrm{NbSe}}_2$. Interestingly, the simplest single-band model has next-nearest-neighbor hopping larger than the nearest-neighbor hopping (by nearly an order of magnitude for ${\mathrm{MoS}}_2$, ${\mathrm{NbSe}}_2$, ${\mathrm{TaSe}}_2$, and ${\mathrm{WS}}_2$), which comes from the cancellation between the atomic on-site terms and the atomic nearest-neighbor hopping after projecting to the obstructed atomic Wannier functions in the underlying three-band model. Furthermore, for ${\mathrm{NbSe}}_2$, we employ a novel approximation scheme to obtain an effective Hamiltonian that captures the three bands originating mainly from the Nb atom. We also use conventional perturbation theory to derive the ab initio obstructed Wannier function with 95% accuracy. Our results pave the way for future study of the effect of quantum geometry on the correlated phases in this family of materials.

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• Electronic structure
• Topological materials
• Topological superconductors
• Monolayer films
• Transition metal dichalcogenides
• Density functional calculations
• Perturbation theory
• Wannier function methods