[Paper Review] Frequency Dependence of the Supersolid Signature in Polycrystalline 4He

George Nichols, M.J. Poole+3 more|arXiv (Cornell University)|Nov 13, 2013

Quantum, superfluid, helium dynamics3 citations

TL;DR

This study investigates the frequency dependence of the supersolid signature in polycrystalline 4He using a two-mode torsional oscillator with widely separated frequencies (5× difference). It finds an unexplained, frequency-dependent complex response in the effective moment of inertia that cannot be accounted for by viscoelasticity or glassy dynamics, suggesting an intrinsic frequency dependence possibly linked to supersolidity in bulk 4He.

ABSTRACT

We report studies, using a two mode torsional oscillator, of the putative supersolid signature in polycrystalline 4He. Measurements at two frequencies enable us to eliminate the viscoelastic contribution to the signature, and other instrumental effects arising from the temperature dependent shear modulus of the sample. The complex response function of the sample, encoded via its effective moment of inertia, shows an unexpected and unexplained frequency dependence. This cannot be accounted for by glassy dynamics within the sample. The results do not rule out the possibility of supersolidity in bulk solid 4He. ?

Motivation & Objective

• To isolate and characterize the supersolid signature in bulk polycrystalline 4He by eliminating instrumental and viscoelastic artifacts.
• To test whether the observed response in torsional oscillators arises from supersolidity or from competing effects such as dislocation dynamics or viscoelasticity.
• To determine if the complex response function of the sample exhibits frequency dependence inconsistent with standard relaxation models.
• To assess whether the observed Cole-Cole plot asymmetry and non-collapsing behavior across frequencies point to a novel quantum response beyond conventional glassy dynamics.

Proposed method

• Employed a compound torsional oscillator with two distinct resonant modes, separated by a factor of five in frequency, to decouple frequency-dependent effects.
• Used a high-aspect-ratio cylindrical sample (14 mm diameter, 2 mm height) to minimize viscoelastic contributions to the response.
• Characterized the sample’s complex response via the effective moment of inertia, $ I_{\text{eff}}(\omega) $, derived from period shifts and dissipation.
• Analyzed the data using Cole-Cole, Davidson-Cole, and special Havriliak-Negami formalisms to identify the functional form of the frequency dependence.
• Compared the oscillator response to shear modulus data from prior studies to distinguish between sample-specific dynamics and intrinsic response mechanisms.
• Applied parametric fitting of the Cole-Cole plots with varying exponents $ s $ to assess the distribution of relaxation times and test model consistency.

Experimental results

Research questions

• RQ1 Does the observed supersolid-like response in polycrystalline 4He exhibit a frequency dependence inconsistent with viscoelastic or glassy relaxation mechanisms?
• RQ2 Can the complex response function of the sample be described by standard relaxation models such as Cole-Cole or Davidson-Cole across two distinct frequencies?
• RQ3 Is the non-collapsing behavior of the Cole-Cole plots across two frequencies indicative of a new physical mechanism beyond dislocation or defect dynamics?
• RQ4 Does the strong asymmetry and extreme aspect ratio of the Cole-Cole plots suggest a fundamental deviation from Debye-like relaxation, possibly pointing to a novel quantum response?
• RQ5 Could the observed frequency dependence be an intrinsic property of supersolidity in bulk 4He at finite temperature, rather than an experimental artifact?

Key findings

• The Cole-Cole plots for the two modes (low and high frequency) do not collapse onto a single curve, indicating a frequency-dependent response that cannot be described by standard relaxation models.
• The data are inconsistent with the Cole-Cole form (which predicts circular chords) and the Davidson-Cole form (which cannot reproduce the observed aspect ratio of ~0.03–0.04).
• Fitting the data with the special Havriliak-Negami form requires exponents $ s = 0.05 $ (low frequency) and $ s = 0.07 $ (high frequency), indicating a very flat distribution of relaxation times in $ \ln \tau $, which is highly unusual.
• The observed frequency dependence cannot be explained by a simple ad hoc frequency scaling $ (\omega / \omega_0)^q $, as it fails to collapse the plots.
• The shear modulus data from Syshchenko et al. (2010), when plotted in Cole-Cole form, are well described by the Davidson-Cole model with $ \gamma = 0.22 $, indicating that the oscillator response is fundamentally different from the elastic response.
• The results suggest that the observed frequency dependence is intrinsic to the sample’s response and may point to a novel mechanism, possibly related to supersolidity, rather than to instrumental or viscoelastic artifacts.