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Register a new userNo Effect of Steady Rotation on Solid $^4$He in a Torsional Oscillator
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We have measured the response of a torsional oscillator containing polycrystalline hcp solid $^{4}$He to applied steady rotation in an attempt to verify the observations of several other groups that were initially interpreted as evidence for macroscopic quantum effects. The geometry of the cell was that of a simple annulus, with a fill line of relatively narrow diameter in the centre of the torsion rod. Varying the angular velocity of rotation up to 2,rad,s$^{-1}$ showed that there were no step-like features in the resonant frequency or dissipation of the oscillator and no history dependence, even though we achieved the sensitivity required to detect the various effects seen in earlier experiments on other rotating cryostats. All small changes during rotation were consistent with those occurring with an empty cell. We thus observed no effects on the samples of solid $^4$He attributable to steady rotation.
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We report measurements of elastic moduli of hcp solid $^4$He down to 15 mK when the samples are rotated unidirectionally. Recent investigations have revealed that the elastic behavior of solid $^4$He is dominated by gliding of dislocations and pinning of them by $^3$He impurities, which move in the solid like Bloch waves (impuritons). Motivated by the recent controversy of torsional oscillator studies, we have preformed direct measurements of shear and Youngs moduli of annular solid $^4$He using pairs of quarter-circle shape piezoelectric transducers (PZTs) while the whole apparatus is rotated with angular velocity $Omega$ up to 4 rad/s. We have found that shear modulus $mu$ is suppressed by rotation below 80 mK, when shear strain applied by PZT exceeds a critical value, above which $mu$ decreases because the shear strain unbinds dislocations from $^3$He impurities. The rotation - induced decrement of $mu$ at $Omega = 4$ rad/s is about 14.7 (12.3) % of the total change of temperature dependent $mu$ for solid samples of pressure 3.6 (5.4) MPa. The decrements indicate that the probability of pinning of $^3$He on dislocation segment, $G$, decreases by several orders of magnitude. We propose that the motion of $^3$He impuritons under rotation becomes strongly anisotropic by the Coriolis force, resulting a decrease in $G$ for dislocation lines aligning parallel to the rotation axis.
The rigid double-torus torsional oscillator (TO) is constructed to reduce any elastic effects in-herent to complicate TO structures, allowing explicit probing for a genuine supersolid signature. We investigated the frequency- and temperature-dependent response of the rigid double-torus TO containing solid 4He with 0.6 ppb 3He and 300 ppb 3He. We did not find evidence to support the frequency-independent contribution proposed to be a property of supersolid helium. The frequency-dependent contribution which comes from the simple elastic effect of solid helium coupled to TO is essentially responsible for the entire response. The magnitude of the period drop is linearly proportional to ${f}^{2}$, indicating that the responses observed in this TO are mostly caused by the overshoot of `soft solid helium against the wall of the torus. Dissipation of the rigid TO is vastly suppressed compared to those of non-rigid TOs.
X-ray diffraction experiments show that solid 4He grown in aerogel is highly polycrystalline, with a hcp crystal structure (as in bulk) and a crystallite size of approximately 100 nm. In contrast to the expectation that the highly disordered solid will have a large supersolid fraction, torsional oscillator measurements show a behavior that is strikingly similar to high purity crystals grown from the superfluid phase. The low temperature supersolid fraction is only ~3x10-4 and the onset temperature is ~ 100 mK.
The non-classical rotational inertia fraction of the identical cylindrical solid $^4$He below 300 mK is studied at 496 and 1173 Hz by a double resonance torsional oscillator. Below 35 mK, the fraction is the same at sufficiently low rim velocities. Above 35 mK, the fraction is greater for the higher than the lower mode. The dissipation peak of the lower mode occurs at a temperature $sim$ 4 mK lower than that of the higher mode. The drive dependence of the two modes shows that the reduction of the fraction is characterized by critical velocity, textit{not} amplitude nor acceleration.
In these torsional oscillator experiments the samples of solid $^4$He were characterized by measuring their thermal conducitvity. Polycrystalline samples of helium of either high isotopic purity or natural concentration of $^3$He were grown in an annular container by the blocked-capillary method and investigated before and after annealing. No correlation has been found between the magnitude of the low-temperature shift of the torsional oscillator frequency and the amount of crystalline defects as measured by the thermal conductivity. In samples with the natural $^3$He concentration a substantial excess thermal conductivity over the usual $T^3$ dependence was observed below 120 mK.
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