Emergent continuous symmetry in anisotropic flexible two-dimensional materials

TL;DR

This paper develops a theory showing that anisotropic flexible 2D materials exhibit an emergent continuous symmetry in their flat phases, leading to universal scaling laws and a line of fixed points, with applications to phosphorene.

Contribution

It introduces a novel theoretical framework revealing emergent continuous symmetry and universal scaling in anisotropic 2D materials with orthorhombic symmetry, applied to phosphorene.

Findings

Existence of an infinite set of flat phases connected by emergent continuous symmetry.

Universal power law scaling of bending rigidity and Young's modulus with momentum.

Application of theory to monolayer black phosphorus (phosphorene).

Abstract

We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. Remarkably, in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale ${\sim} 10\, {\rm nm}$, these materials possess an infinite set of flat phases which are connected by emergent continuous symmetry. This hidden symmetry leads to the formation of a stable line of fixed points corresponding to different phases. The same symmetry also enforces power law scaling with momentum of the anisotropic bending rigidity and Young's modulus, controlled by a single universal exponent -- the very same along the whole line of fixed points. These anisotropic flat phases are uniquely labeled by the ratio of absolute Poisson's ratios. We apply our theory to monolayer black phosphorus (phosphorene).