Transition into the Supersolid (SS) State, Supersolid Density ρ _ss and the Critical Velocity V _c to Destroy the SS State

Abstract

We have reported the onset of the vortex fluid (VF) state in hcp solid ⁴He below an onset temperature T _o (Penzev et al. in Phys. Rev. Lett. 101:065301, 2008). We have also shown the transition from the VF state into the supersolid (SS) state, which is characterized by a supersolid density and macroscopic coherence, below a transition (Kubota et al. in J. Low Temp. Phys. 158:572, 2010; Shimizu et al. in arXiv:0903.1326, 2009; Yagi et al. in J. Low Temp. Phys., QFS2010, 2011) at T _c , as well as a critical velocity for the destruction of the SS state. Here we describe further confirming evidence of the phase transition into the SS state, namely, we report here some other observations than the hysteretic behavior. We find some other features which indicate a clear change of the properties in the hcp ⁴He below the same T _c as hysteretic behavior, reported in Kubota et al. (J. Low Temp. Phys. 158:572, 2010), Shimizu et al. (arXiv:0903.1326, 2009), Yagi et al. (J. Low. Temp. Phys., QFS2010, 2011). It was discovered by detailed study of the torsional oscillator (TO) drive velocity V _ac dependence of the nonlinear rotational susceptibility (NLRS) of the VF state. We discuss the features of the VF to SS transition. The large ratio between T _o and T _c may indicate large fluctuations of the system and it may give a basis for the vortex state (Fisher et al. in Phys. Rev. B 43(1):130, 1991) appearance in the hcp ⁴He, as seen in the new type of superconductors. We discuss a question related to the observation of the VF phase with specific dynamic features (Nemirovskii et al. in arXiv:0907.0330, 2009), coexisting with the SS phase and a possible new kind of phase transition coexisting with the SS phase and a possible new kind of phase transition for the VF to SS transition.