Absolute Poisson's ratio and the bending rigidity exponent of a crystalline two-dimensional membrane

Abstract

We compute the absolute Poisson's ratio $\nu$ and the bending rigidity exponent $\eta$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d=2+d_c$, $d_c\gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the absolute Poisson's ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $\nu =-1+2/d_c-a/d_c^2+\dots$ where $a\approx 1.76\pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $\eta =2/d_c+(73-68\zeta (3))/(27d_c^2)+\dots$. These results cannot be captured by self-consistent screening approximation.

References in corpus (11)

• Self-Consistent Theory of Polymerized Membranes
• The Effect of Intrinsic Crumpling on the Mechanics of Free-Standing Graphene
• Crumpling transition and flat phase of polymerized phantom membranes
• Scaling behavior and strain dependence of in-plane elastic properties of graphene
• Response of thermalized ribbons to pulling and bending
• The Flat Phase of Crystalline Membranes
• The Structure of Physical Crystalline Membranes within the Self-Consistent Screening Approximation
• Anomalous elasticity, fluctuations and disorder in elastic membranes
• Rippling and crumpling in disordered free-standing graphene
• Differential Poisson's ratio of a crystalline two-dimensional membrane
• Nonlocal effective average action approach to crystalline phantom membranes

Cited by in corpus (12)

• Thermalized buckling of isotropically compressed thin sheets
• Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach
• The flat phase of polymerized membranes at two-loop order
• Scale without conformal invariance in membrane theory
• Three-loop order approach to flat polymerized membranes
• Disorder-induced rippled phases and multicriticality in free-standing graphene
• Thermal ripples in bilayer graphene
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Emergent continuous symmetry in anisotropic flexible two-dimensional materials
• 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
• Perturbative renormalization and thermodynamics of quantum crystalline membranes