Geometric Frustration in a Monolayer TMD Alloy

Geometric frustration occurs when the constituent interactions of a system cannot be simultaneously satisfied due to the underlying geometry. In an idealized frustrated system, long-range order is prevented, and degenerate ground-states with short-range order are observed, leading to extensive entropy at 0 K. In real materials, higher-order effects can lead to relieving of frustration, allowing long-range order to appear. Here, we directly observe frustrated ordering of the atomic species in a monolayer transition metal dichalcogenide (TMD) alloy, using scanning transmission electron microscopy (STEM). We find that this system is analogous to the 2D Ising model of antiferromagnetic spins in a triangular lattice, and long-range order is thoroughly suppressed. Using density functional theory, we build a lattice model that closely matches the statistical properties of the experimental atomic distribution. We also demonstrate the effects of atomic ordering on the band structure. We predict that the degree of ordering can be controlled by the growth temperature, allowing the tuning of the electronic, optical and thermal properties.