Squeezing superfluid from a stone: Coupling superfluidity and elasticity in a supersolid

Superfluidity---the ability of liquid $^4$He, when cooled below 2.176 K, to flow without resistance through narrow pores---has long served as a paradigm for the phenomenon of ``off-diagonal long-range order'' (ODLRO) in quantum liquids and superconductors. Supersolidity---the coexistence of ODLRO with the crystalline order of a solid---was proposed theoretically over 35 years ago as an even more exotic phase of solid $^4$He, but it has eluded detection. Recently, Kim and Chan [1,2] have reported an anomalous decoupling transition of solid $^4$He in a torsional oscillator measurement, and interpret their results as evidence for non-classical rotational inertia and a possible supersolid phase of $^4$He. In this talk I will give brief historical review of the theory of and experimental searches for supersolidity. I will then discuss a phenomenological Landau theory of the normal solid to supersolid (NS-SS) transition in which superfluidity is coupled to the elasticity of the crystalline $^4$He lattice, and underscore the implications of this theory for experimental searches for supersolidity [3]. I will also discuss a hydrodynamic model for supersolids, in which the additional broken gauge symmetry in the supersolid phase produces a collective mode that is analogous to second sound in superfluid helium. \newline \newline [1] E. Kim and M. H. W. Chan, Nature (London) \textbf{427}, 225 (2004). \newline [2] E. Kim and M. H. W. Chan, Science \textbf{305}, 1941 (2004). \newline [3] A. T. Dorsey, P. M. Goldbart, and J. Toner, ``Squeezing superfluid from a stone: Coupling superfluidity and elasticity in a supersolid,'' Phys. Rev. Lett. \textbf{96}, 055301 (2006).