Dislocation Mobility and Anomalous Shear Modulus Effect in $^4$He Crystals

TL;DR

This paper models dislocation mobility in solid $^4$He considering a superfluid field along dislocation lines, explaining the anomalous shear modulus drop at low temperatures through superfluid-related damping effects.

Contribution

It introduces a superfluid field model for dislocation dynamics in solid $^4$He, linking superfluidity to shear modulus anomalies and providing quantitative agreement with experiments.

Findings

Superfluid field influences dislocation mobility and damping.

Shear modulus drops sharply when superfluid disappears with increasing temperature.

Model aligns with experimental shear modulus behavior in solid $^4$He.

Abstract

We calculate the dislocation glide mobility in solid $^4$He within a model that assumes the existence of a superfluid field associated with dislocation lines. Prompted by the results of this mobility calculation, we study within this model the role that such a superfluid field may play in the motion of the dislocation line when a stress is applied to the crystal. To do this, we relate the damping of dislocation motion, calculated in the presence of the assumed superfluid field, to the shear modulus of the crystal. As the temperature increases, we find that a sharp drop in the shear modulus will occur at the temperature where the superfluid field disappears. We compare the drop in shear modulus of the crystal arising from the temperature dependence of the damping contribution due to the superfluid field, to the experimental observation of the same phenomena in solid $^4$He and find quantitative agreement. Our results indicate that such a superfluid field plays an important role in dislocation pinning in a clean solid $^4$He at low temperatures and in this regime may provide an alternative source for the unusual elastic phenomena observed in solid $^4$He.