Modified Granato-Lucke Theory with Pinning Length Distribution in Solid He-4

Abstract

We developed a detailed microscopic method that describes the shear modulus anomaly of solid helium at low temperature. The shear modulus was calculated using the pinning length of dislocations determined in detail for both crossing network nodes and He-3 impurities. The strong suppression of the shear modulus is reproduced well as the temperature or stress increases. The shear modulus at low temperatures depends strongly on how the state was prepared. All the key features in the stress hysteresis can be quantitatively explained in terms of the thermomechanical path-dependent pinning length of dislocation networks.