Pinning of a two-dimensional membrane on top of a patterned substrate: the case of graphene

Abstract

We study the pinning of a two-dimensional membrane to a patterned substrate within elastic theory both in the bending rigidity and in the strain dominated regimes. We find that both the in-plane strains and the bending rigidity can lead to depinning. We show from energetic arguments that the system experiences a first order phase transition between the attached configuration to a partially detached one when the relevant parameters of the substrate are varied, and we construct a qualitative phase diagram. Our results are confirmed through analytical solutions for some simple geometries of the substrate's profile.

Minor changes. Final version, as published

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• Gaussian deformations in graphene ribbons: flowers and confinement
• Nonlinear phononics using atomically thin membranes
• Density functional theory analysis of flexural modes, elastic constants, and corrugations in strained graphene
• The sensitivity of Graphene 'Snap-through' to substrate geometry
• Convenient Peierls phase choice for periodic atomistic systems under magnetic field
• Thermal buckling transition of crystalline membranes in a field
• Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures
• Avoidance and Coalescence of Delamination Patterns
• Emergent space-time supersymmetry at disorder quantum critical point
• Pseudo Electric Field and Pumping Valley Current in Graphene Nano-bubbles