Quantum loops in the 1T transition metal dichalcogenides

Loop arrangements and their quantum superpositions describe several interesting many-particle states. We propose that they also describe bonding in a class of transition metal dichalcogenides. We present an effective quantum loop model for monolayers with 1T structure and a d${}^2$ valence electron configuration: materials of the form MX${}_2$ (M = Mo, W and X=S, Se, Te) and AM${}^{\mathrm{\prime }}$Y${}_2$ (A = Li, Na; M${}^{\mathrm{\prime }}$ = V, Nb and Y = O, S, Se). Their t${}_{2g}$ orbitals exhibit strongly directional overlaps between neighbouring atoms, favouring the formation of valence bonds. A transition metal atom forms two valence bonds, each with one of its neighbours. When connected, these bonds form loops that cover the triangular lattice. We construct a minimal Rokhsar-Kivelson-like model with resonance processes that cut and reconnect loops that run in proximity. The resulting dynamics is more constrained than in traditional quantum dimer models, with a `bending’ constraint that arises from orbital structure. In the resulting phase diagram, we find phases that resemble distorted phases seen in materials, viz., the 1T${}^{\mathrm{\prime }}$ and trimerized phases. As a testable prediction, we propose that a single d${}^1$ or d${}^3$ impurity will terminate a loop and give rise to a long-ranged texture. For example, a Ti/Cr defect in LiVO${}_2$ will produce one or more domain walls that propagate outward from the impurity. We discuss the possibility of a loop liquid phase that can emerge in these materials.