Thermal buckling transition of crystalline membranes in a field

Abstract

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.

arXiv comment5 pages (main text) + 25 pages (supplementary material), 3 figures; a published version for PRL, with minor edits and added references

References in corpus (30)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• The structure of suspended graphene sheets
• Macroscopic graphene membranes and their extraordinary stiffness
• Self-Consistent Theory of Polymerized Membranes
• Crumpling transition and flat phase of polymerized phantom membranes
• Scaling behavior and strain dependence of in-plane elastic properties of graphene
• Electron-hole puddles in the absence of charged impurities
• The Structure of Physical Crystalline Membranes within the Self-Consistent Screening Approximation
• Anomalous elasticity, fluctuations and disorder in elastic membranes
• Gauge fields, ripples and wrinkles in graphene layers
• A New Phase of Tethered Membranes: Tubules
• Pinning of a two-dimensional membrane on top of a patterned substrate: the case of graphene
• Fluctuating shells under pressure
• Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene
• Rippling and crumpling in disordered free-standing graphene
• Elasticity, Shape Fluctuations and Phase Transitions in the New Tubule Phase of Anisotropic Tethered Membranes
• Statistical mechanics of thin spherical shells
• First order phase transitions in polymerized phantom membranes
• Differential Poisson's ratio of a crystalline two-dimensional membrane
• Buckling of thermalized elastic sheets
• Universal Elasticity and Fluctuations of Nematic Gels
• Thermal fluctuations and anomalous elasticity of homogeneous nematic elastomers
• Nonlinear Elasticity, Fluctuations and Heterogeneity of Nematic Elastomers
• The flat phase of polymerized membranes at two-loop order
• Thermal buckling and symmetry breaking in thin ribbons under compression
• Thermal stiffening of clamped elastic ribbons
• Phases and Transitions in Phantom Nematic Elastomer Membranes
• Ferromagnetic transition in a one-dimensional spin-orbit-coupled metal and its mapping to a critical point in smectic liquid crystals
• Anomalous Hooke's law in disordered graphene

Cited by in corpus (8)

• Thermalized buckling of isotropically compressed thin sheets
• Lifshitz gauge duality
• Spontaneous tilt of single-clamped thermal elastic sheets
• Emergent continuous symmetry in anisotropic flexible two-dimensional materials
• Buckling in a rotationally invariant spin-elastic model
• Thermalized buckling of extensible, semiflexible polymers
• A molecular dynamics simulation of thermalization of crystalline lattice with harmonic interaction
• Emergent dynamic stress regulators via coordinated thermal fluctuations and stress in harmonic crystalline lattices