Squeezing Superfluid from a Stone: Coupling Superfluidity and Elasticity in a Supersolid

Starting from the assumption that the normal solid to supersolid (NS-SS) phase transition is continuous, we develop a phenomenological Landau theory of the transition in which superfluidity is coupled to the elasticity of the crystalline ${}^4\mathrm{He}$ lattice. We find that the elasticity does not affect the universal properties of the superfluid transition, so that in an unstressed crystal the well-known $\lambda$ anomaly in the heat capacity of the superfluid transition should also appear at the NS-SS transition. We also find that the onset of supersolidity leads to anomalies in the elastic moduli and thermal expansion coefficients near the transition and, conversely, that inhomogeneous lattice strains can induce local variations of the superfluid transition temperature, leading to a broadened transition.