Thermal fluctuations of free standing graphene

Abstract

We use non-perturbative renormalization group techniques to calculate the momentum dependence of thermal fluctuations of graphene, based on a self-consistent calculation of the momentum dependent elastic constants of a tethered membrane. We find a sharp crossover from the perturbative to the anomalous regime, in excellent agreement with Monte Carlo results for graphene, and give an accurate value for the crossover scale. Our work strongly supports the notion that graphene is well described as a tethered membrane. Ripples emerge naturally from our analysis.

5 pages, 2 figures; discussion of the Ginzburg scale of the out-of-plane fluctuations and its relation to ripples was extended. Final version, to appear in PRB

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Cited by in corpus (40)

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• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene
• Non-Hookean statistical mechanics of clamped graphene ribbons
• Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
• Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene
• Rippling and crumpling in disordered free-standing graphene
• The effect of rippling on the mechanical properties of graphene
• Thermodynamics of quantum crystalline membranes
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• First order phase transitions in polymerized phantom membranes
• Functional renormalization group approach to interacting bosons at zero temperature
• Nonlocal effective average action approach to crystalline phantom membranes
• High Precision Fourier Monte Carlo Simulation of Crystalline Membranes
• Flexuron, a self-trapped state of electron in crystalline membranes
• Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond epsilon-expansion
• Thermal crumpling of perforated two-dimensional sheets
• Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach
• A glassy phase in quenched disordered graphene and crystalline membranes
• The flat phase of polymerized membranes at two-loop order
• The flat phase of quantum polymerized membranes
• Thermal stiffening of clamped elastic ribbons
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• Three-loop order approach to flat polymerized membranes
• Fourier Monte Carlo Renormalization Group Approach to Crystalline Membranes
• From the 2D graphene honeycomb lattice to 1D nanoribbons: dimensional crossover signals in the structural thermal fluctuations
• Disorder-induced rippled phases and multicriticality in free-standing graphene
• Interplay between nanometer-scale strain variations and externally applied strain in graphene
• Effective average action based approach to correlation functions at finite momenta
• Wrinkling transition in quenched disordered membranes at two loops
• Universal behaviors in the wrinkling transition of disordered membranes
• Interplay of topology and geometry in frustrated 2d Heisenberg magnets
• Flat phase of quenched disordered membranes at three-loop order
• Stiffening Thermal Membranes by Cutting
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Reply to 'Comment on "Thermodynamics of quantum crystalline membranes"'
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Renormalization group approach to the elastic properties of graphene bilayers