Effect of anomalous elasticity on bubbles in van der Waals heterostructures

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 nonlinear plate theory as well as the 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-range interaction of relevant thermal fluctuations (flexural phonons), is responsible for the nonlinear Hooke law observed recently in graphene. It is shown that this anomalous elasticity affects the dependence of the maximal height of the bubble as a function of its radius and temperature. We determine 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 room temperature.