  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.
