Nonconventional screening of Coulomb interaction in two-dimensional semiconductors and metals: A comprehensive constrained random phase approximation study of MX2 (M=Mo, W, Nb, Ta; X=S, Se, Te)

Experimental observations of large exciton binding energies and\nnon-hydrogenic Rydberg series in 2D semiconducting TMDs, along with deviations\nin plasmon dispersion in 2D metallic TMDs, suggest the presence of a\nnonconventional screening of the Coulomb interaction. The experimentally\nobserved Mott insulating state in the charge density wave (CDW) reconstructed\nlattice of TMDs containing 4d and 5d elements further confirms the presence of\nstrong Coulomb interactions in these systems. In this study, we use\nfirst-principles electronic structure calculations and constrained random-phase\napproximation to calculate the Coulomb interaction parameters (partially\nscreened U and fully screened W) between localized $d$ electrons in 2D TMDs. We\nspecifically explore materials represented by the formula MX2 (M=Nb, Ta, Mo, W,\nand X=S, Se, Te) and consider three different phases (1H, 1T, and 1T'). Our\nresults show that the short-range interactions are strongly screened in all\nthree phases, whereas the long-range interactions remain significant even in\nmetallic systems. This nonconventional screening provides a compelling\nexplanation for the deviations observed in the usual hydrogenic Rydberg series\nand conventional plasmon dispersion in 2D semiconducting and metallic TMDs,\nrespectively. Our calculations yield on-site Coulomb interaction parameters U\nwithin the ranges of 0.8-2.5 eV, 0.8-1.9 eV, and 0.9-2.4 eV for the 1H, 1T, and\n1T' structures, respectively. Furthermore, our findings indicate a\nsubstantially high ratio of on-site effective Coulomb interaction to bandwidth\n(U_eff/W_b >> 1) in CDW TMDs, providing robust evidence for the experimentally\nobserved strongly correlated Mott phase.\n