Torsional oscillators and the entropy dilemma of putative supersolid⁴He

Abstract

Solid 4 He is viewed as a nearly perfect Debye solid. Yet, recent calorimetry measurements by the PSU group (J. Low Temp. Phys. 138, 853 (2005) and Nature 449, 1025 (2007)) indicate that at low temperatures the specific heat has both cubic and linear contributions. These features appear in the same temperature range where measurements of the torsional oscillator period suggest a supersolid transition. We analyze the specific heat and compare the measured with the estimated entropy for a proposed supersolid transition with 1% superfluid fraction and find that the observed entropy is too small. We suggest that the low-temperature linear term in the specific heat is due to a glassy state that develops at low temperatures and is caused by a distribution of tunneling systems in the crystal. We propose that dislocation related defects produce those tunneling systems. Further, we argue that the reported putative mass decoupling, that means an increase in the oscillator frequency, is consistent with a glass-like transition. The glass scenario offers an alternative interpretation of the torsional oscillator experiments in contrast to the supersolid scenario of nonclassical rotational inertia.

A Glassy Contribution to the Heat Capacity of hcp 4He Solids

“…Our results show that the low-temperature deviations in the measured specific heat can be explained by contributions from a glassy fraction of the solid. These results add further support to our previous interpretation of torsion oscillator experiments in terms of a backaction due to a glassy subsystem, which is possibly present in solid 4 He [38,37,39]. …”

“…This enormous discrepancy between supersolid fractions in specific heat and torsion oscillator experiments was already noticed in Refs. [36,37]. Until to date, this discrepancy remains a major puzzle that is hard to reconcile within a purely supersolid scenario.…”

“…While there is still no clear evidence of transition in the melting curve experiments, recent pressure measurements and specific heat measurements have both shown deviations from the expected pure Debye lattice behavior. Balatsky and coworkers [36,37] argued that the deviations occurring at low temperatures might be related to a glass phase, where the role of two-level systems could be taken by tunneling dislocation loop segments. This description is also accompanied by an argument that the excess entropy associated with the deviation is too small for supersolidity to lead to detectable mechanical effects, if it is due to a supersolid fraction alone.…”

Phenomenological Ginzburg-Landau theory for supersolidity

“…In Ref. 44, it is claimed that specific-heat measurements are contrary to entropy predictions based on a Bose-Einstein type of supersolidity, however, we may see that in our GinzburgLandau model there is no such problem. 3 is of the order of 10 −4 .…”

Effects ofHe3impurity on solidHe4studied by compo

“…Nussinov et al 30 and Graf et al 37 have carried out much more sophisticated analyses of observed TO responses with generalized rotational susceptibilities expressing glassy response. They found that various single frequency TO responses in both dissipation and frequency shift could be fitted by appropriately adjusting parameters in the glassy response model.…”