The effect of anomalous elasticity on the bubbles in van der Waals heterostructures

TL;DR

This paper investigates how anomalous elasticity, caused by thermal fluctuations, influences the shape and thermodynamics of bubbles in van der Waals heterostructures, with specific focus on graphene.

Contribution

It extends existing membrane and plate theories to include scale-dependent elastic properties due to thermal fluctuations, revealing new effects on bubble behavior.

Findings

Anomalous elasticity alters the bubble height-radius relationship.

The characteristic temperature for elasticity effects is identified.

Predicted effects are experimentally accessible at room temperature for graphene.

Abstract

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the non-linear plate theory as well as membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence caused by long-ranged interaction of relevant thermal fluctuations (flexural phonons), is responsible for the anomalous Hooke's law observed recently in graphene. It is shown that this anomalous elasticity affects dependence of the maximal height of the bubble on its radius and temperature. We identify the characteristic temperature above which the anomalous elasticity is important. It is suggested that for graphene-based van der Waals heterostructures the predicted anomalous regime is experimentally accessible at the room temperature.