Emergent continuous symmetry in anisotropic flexible two-dimensional materials

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 $\sim 10\mathrm{nm}$, 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).

9 pages, 3 figures

References in corpus (10)

• Electric Field Effect in Atomically Thin Carbon Films
• The Renaissance of Black Phosphorus
• Superior mechanical flexibility of phosphorene and few-layer black phosphorus
• Auxetic Black Phosphorus: A 2D Material with Negative Poisson's Ratio
• Recent Advances in Two-Dimensional Metal Monochalcogenides
• Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
• Statistical mechanics of thin spherical shells
• Thermal buckling transition of crystalline membranes in a field
• Scale without conformal invariance in membrane theory
• Effect of flexural phonons on the hole states in single-layer black phosphorus

Cited by in corpus (3)

• Unconventional mechanical and thermal behaviors of MOF CALF-20
• Anisotropic effects in two-dimensional materials
• Disorder-driven transition to tubular phase in anisotropic two-dimensional materials