Two-dimensional (2D) semiconducting and metallic transition metal dichalcogenides (TMDs) have attracted significant attention for their promising applications in a variety of fields. Experimental observations of large exciton binding energies and nonhydrogenic Rydberg series in 2D semiconducting TMDs, along with deviations in plasmon dispersion in 2D metallic TMDs, suggest the presence of a nonconventional screening of the Coulomb interaction. The experimentally observed Mott insulating state in the charge density wave (CDW) reconstructed lattice of TMDs containing $4d$ and $5d$ elements further confirms the presence of strong Coulomb interactions in these systems. In this study, we use first-principles electronic structure calculations and constrained random-phase approximation to calculate the Coulomb interaction parameters (partially screened $U$ and fully screened $W$) between localized $d$ electrons in 2D TMDs. We specifically explore materials represented by the formula ${MX}_2$ $(M=\mathrm{Nb}, \mathrm{Ta}, \mathrm{Mo}, \mathrm{W}; X=\mathrm{S}, \mathrm{Se}, \mathrm{Te})$ and consider three different phases $(1H, 1T, \text{and} 1T^{\prime })$. Our results show that the short-range interactions are strongly screened in all three phases, whereas the long-range interactions remain significant even in metallic systems. This nonconventional screening provides a compelling explanation for the deviations observed in the usual hydrogenic Rydberg series and conventional plasmon dispersion in 2D semiconducting and metallic TMDs, respectively. Our calculations yield on-site Coulomb interaction parameters $U$ within the ranges of 0.8–2.5, 0.8–1.9, and 0.9–2.4 eV for the $1H$, $1T$, and $1T^{\prime }$ structures, respectively. These values depend on the specific chalcogen X, the number of $d$ electrons, and the correlated subspace. Using the calculated $U$ parameters for the undistorted $1T$ structure, we extract the on-site effective $U_{00}^{\mathrm{eff}}$ and nearest-neighbor $U_{01}^{\mathrm{eff}}$ Coulomb interaction parameters for reconstructed commensurate CDW $\mathrm{Nb}{X}_2$ and $\mathrm{Ta}{X}_2$ compounds. Furthermore, our findings indicate a substantially high ratio of on-site effective Coulomb interaction to bandwidth $(U_{00}^{\mathrm{eff}}/W_b\gg 1)$ in CDW TMDs, providing robust evidence for the experimentally observed strongly correlated Mott phase. This work sheds light on the nonconventional screening of Coulomb interactions in 2D TMDs, offering valuable insights into their electronic properties and potential applications in emerging technologies. It advances our fundamental understanding of these materials and holds promise for their use in various applications.

• Received 13 November 2023
• Revised 31 January 2024
• Accepted 20 February 2024

DOI:https://doi.org/10.1103/PhysRevB.109.125108