Elastic anisotropies and long-ranged interactions in solid membranes

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.

Thermal Buckling Transition of Crystalline Membranes in a Field

Two-dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant, e.g., for graphene. Here we study their thermal fluctuations in the absence of exact rotational invariance in the embedding space. An example is provided by a membrane in an orientational field, tuned to a critical buckling point by application of in-plane stresses. Through a detailed analysis, we show that the transition is in a new universality class. The self-consistent screening method predicts a second-order transition, with modified anomalous elasticity exponents at criticality, while the RG suggests a weakly first-order transition.