A glassy phase in quenched disordered graphene and crystalline membranes

Abstract

We investigate the flat phase of $D$-dimensional crystalline membranes embedded in a $d$-dimensional space and submitted to both metric and curvature quenched disorders using a nonperturbative renormalization group approach. We identify a second order phase transition controlled by a finite-temperature, finite-disorder fixed point unreachable within the leading order of $\epsilon =4-D$ and $1/d$ expansions. This critical point divides the flow diagram into two basins of attraction: that associated to the finite-temperature fixed point controlling the long distance behaviour of disorder-free membranes and that associated to the zero-temperature, finite-disorder fixed point. Our work thus strongly suggests the existence of a whole low-temperature glassy phase for quenched disordered graphene, graphene-like compounds and, more generally, crystalline membranes.

6 pages, 1 figure

References in corpus (13)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Exact evolution equation for the effective potential
• Theory of 2D crystals: graphene and beyond
• Crumpling transition and flat phase of polymerized phantom membranes
• Suppression of anharmonicities in crystalline membranes by external strain
• Graphene as a Prototype Crystalline Membrane
• Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene
• Thermal fluctuations of free standing graphene
• Nonlocal effective average action approach to crystalline phantom membranes
• The flat phase of quantum polymerized membranes
• The random anisotropy model revisited
• First-order phase transitions in spinor Bose gases and frustrated magnets

Cited by in corpus (19)

• The nonperturbative functional renormalization group and its applications
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach
• The flat phase of polymerized membranes at two-loop order
• Three-loop order approach to flat polymerized membranes
• Disorder-induced rippled phases and multicriticality in free-standing graphene
• Thermal ripples in bilayer graphene
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Wrinkling transition in quenched disordered membranes at two loops
• Emergent continuous symmetry in anisotropic flexible two-dimensional materials
• Universal behaviors in the wrinkling transition of disordered membranes
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Flat phase of quenched disordered membranes at three-loop order
• Disorder-driven transition to tubular phase in anisotropic two-dimensional materials
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Geometrically-induced localization of flexural waves on thin warped physical membranes
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Renormalization group approach to the elastic properties of graphene bilayers