Shear modulus in viscoelastic solid $^4$He

TL;DR

This paper models the shear modulus anomaly in solid $^4$He as a viscoelastic response with a VFT relaxation time, predicting frequency-independent maximum changes and matching experimental data.

Contribution

It introduces a viscoelastic model with multiphase components and VFT relaxation to explain the shear modulus anomaly in solid $^4$He, aligning theory with experiments.

Findings

Shear modulus stiffening is described by a viscoelastic component with increasing relaxation time.

Maximum shear modulus change and dissipation peak are frequency-independent.

Vogel-Fulcher-Tammann relaxation time fits experimental data.

Abstract

The complex shear modulus of solid $^4$He exhibits an anomaly in the same temperature region where torsion oscillators show a change in period. We propose that the observed stiffening of the shear modulus with decreasing temperature can be well described by a viscoelastic component that possesses an increasing relaxation time as temperature decreases. Since a glass is a viscoelastic material, the response functions derived for a viscoelastic material are identical to those obtained for a glassy component due to a time delayed restoring back-action. By generalizing the viscoelastic equations for stress and strain to a multiphase system of constituents, composed of patches with different damping and relaxation properties, we predict that the maximum change of the magnitude of the shear modulus and the maximum height of the dissipation peak are independent of an applied external frequency. The same response expressions allow us to calculate the temperature dependence of the shear modulus' amplitude and dissipation. Finally, we demonstrate that a Vogel-Fulcher-Tammann (VFT) relaxation time is in agreement with available experimental data.