Quantized Vortex Physics in hcp Solid 4He and Supersolid Transition Studied by Torsional Oscillator Technique
Kubota Group
Superfluidity has been found not only in the Bose fluid, liquid 4He and Fermi fluids, liquid 3He and conduction electrons in metals, but also in dilute gaseous materials. Superfluidity had been considered in the early days primarily as a result of Bose Einstein Condensation (BEC) of the constituent particles, which can exchange positions with each other. The original discussions as to the possibility of observing the “supersolidity”, or superfluidity in a solid were initiated in 1956 by Penrose and Onsager with a negative result, and positive discussions have gained strength in 1960’s, when experimental evidence of quantized circulation, as well as quantized flux in superconductors were discovered. It was 1972 when Kosterlitz and Thouless proposed a topological two dimensional transition, describing a 2D superfluid transition at a finite temperature TKT, involving 2D vortex anti-vortex pairs. Its realization was experimentally clearly shown by the study of a superfluid transition in a monolayer of He by Bishop and Reppy. We have been studying a series of artificial 3D superfluids in monolayers of He condensed on well controlled, porous glass substrates with fixed diameters [1]. We could show 3D vortex excitations in such a system both by theory [2] and experiments [3].
Here we report on our recent quantized vortex physics in hcp solid 4He studied by detailed measurements of torsional oscillator responses under AC and DC rotation and evidence of the new features of the supersolid state as well as the quantized vortex state in this quantum solid, while quite a large number of people still try to understand the reported properties without involvement of quantized vortices or superfluidity in the solid, but by discussing classical responses of dislocations or glassy properties of the solid.
Our publication [4] discussed the onset of the vortex fluid(VF) state [5], pointing out the sudden start of non-linear response of the torsional oscillator(TO) with hcp 4He samples in response to delicate change of the drive velocity Vac. We discussed also the logVac linear decrease of the non linear rotational susceptibility, NLRS and its temperature, T dependent change, as the evidence of the VF state [4]. Further detailed analysis [6] displayed in Fig. 1 indicates a peculiar change of the logVac linear slope at a certain Vac value for a specific T. The turning Vac points as well as corresponding NLRS points are plotted in Fig. 2 as a function of 1/T2. We observe a jump between 1/T2 ~2 and ~3 x10-4 K-2, for temperatures in the range ~58 mK and ~71 mK, which coincides with our earlier report[7] of the appearance of a hysteretic component below Tc ~75mK(see Fig.3) and the proposal of the order parameter of the supersolid state [7].
The macroscopic coherence of the supersolid(SS) state is probably revealed below the same Tc, by our TO response study[8] of the vortex lines penetration under DC rotation. Its data are inter-compared with the hysteretic component T dependence in Fig. 3. And we display the hysteretic component of the SS state and the VF state NLRS (Vac→0) in Fig.4 [6] in the unit of % of the solid He total mass, proposing that NLRShys is actually the supersolid density ρss itself. These TO experiments have been performed using a supreme rotating cryostat built by Kubota group [9].
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