Atomically asymmetric inversion scales up to mesoscopic single-crystal monolayer flakes

Symmetry is highly relevant with various quantities and phenomena in physics. While the translational symmetry breaks at the edges of two-dimensional hexagonal crystalline flakes, it is usually associated with the breaking of central inversion symmetry that is yet to be observed in terms of physical properties. Here, we report an experiment-theory joint study on inplane compressed single-crystal monolayer WS2 flakes. Although the flakes show a hexagonal appearance with a C6 symmetry, our density functional theory calculations predict that their in-plane strain, geometric structure, work-function, energy bandgap, and mechanical modulus are nonequivalent among the triangular regions with different edge terminations at the atomic scale, and the flakes exhibit self-patterns with a C3 symmetry. Such nonequivalence of physical properties and concomitant self-patterns persist even in a 50 μm-sized monolayer WS2, observed using atomic force microscopy. This indicates that the symmetry arising from the atomic geometry could preserve up to tens of microns for both geometric and properties of the flake, regardless of its mesoscopic geometry, i.e., C6 here. Such a detectable mesoscopic scale and symmetric nano- to mesoscale patterns provide promising building blocks for 2D materials and devices and also allow edge terminations of 2D flakes to be directly distinguished.