Unified picture of lattice instabilities in metallic transition metal dichalcogenides

Abstract

Transition metal dichalcogenides (TMDs) in the $1T$ polymorph are subject to a rich variety of periodic lattice distortions, often referred to as charge-density waves (CDWs) when not too strong. We study from first principles the fermiology and phonon dispersion of three representative single-layer transition metal disulfides with different occupation of the ${t}_{2g}$ subshell: ${\mathrm{TaS}}_{2}\phantom{\rule{4pt}{0ex}}({t}_{2g}^{1}),{\mathrm{WS}}_{2}\phantom{\rule{4pt}{0ex}}({t}_{2g}^{2})$, and ${\mathrm{ReS}}_{2}\phantom{\rule{4pt}{0ex}}({t}_{2g}^{3})$ across a broad range of doping levels. While strong electron-phonon interactions are at the heart of these instabilities, we argue that away from half-filling of the ${t}_{2g}$ subshell, the doping dependence of the calculated CDW wave vector can be explained from simple fermiology arguments, so that a weak-coupling nesting picture is a useful starting point for understanding. On the other hand, when the ${t}_{2g}$ subshell is closer to half-filling, we show that nesting is irrelevant, while a real-space strong-coupling picture of bonding Wannier functions is more appropriate and simple bond-counting arguments apply. Our study thus provides a unifying picture of lattice distortions in $1T$ TMDs that bridges the two regimes, while the crossover between these regimes can be attained by tuning the filling of the ${t}_{2g}$ orbitals.