Emergent Continuous Symmetry in Anisotropic Flexible Two-Dimensional Materials

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 ∼10 nm , these materials possess an infinite set of flat phases. These phases corresponds to a stable line of fixed points and are connected by an emergent continuous symmetry. This symmetry 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 phosphorene.