Pinning of a two-dimensional membrane on top of a patterned substrate: the case of graphene
arXiv:1007.1017 · doi:10.1103/PhysRevB.83.165405
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.
arXiv commentMinor changes. Final version, as published
References in corpus (22)
- Electric Field Effect in Atomically Thin Carbon Films
- The electronic properties of graphene
- Two-Dimensional Gas of Massless Dirac Fermions in Graphene
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Ultrahigh electron mobility in suspended graphene
- The structure of suspended graphene sheets
- Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer
- Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2
- Intrinsic ripples in graphene
- Atomic Structure of Graphene on SiO2
- Carrier transport in 2D graphene layers
- Strong suppression of weak (anti)localization in graphene
- High-Resolution Scanning Tunneling Microscopy Imaging of Mesoscopic Graphene Sheets on an Insulating Surface
- Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
- Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO2
- Continuum elastic modeling of graphene resonators
- Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
- Electrostatic interactions between graphene layers and their environment
- Substrate-regulated morphology of graphene
- Supported Membranes on Chemically Structured and Rough Surfaces
- Snap-through instability of graphene on substrates
- Singular elastic strains and magnetoconductance of suspended graphene
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