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

TL;DR

This paper investigates how a two-dimensional membrane like graphene interacts with a patterned substrate, revealing phase transitions between pinned and detached states driven by elastic properties and substrate features.

Contribution

It introduces a theoretical framework analyzing membrane pinning on patterned substrates, identifying phase transitions and providing analytical solutions for specific geometries.

Findings

First order phase transition between pinned and detached states.

Both in-plane strains and bending rigidity influence depinning.

Qualitative phase diagram constructed for membrane-substrate interaction.

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.