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

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.

Superfluid field response to edge dislocation motion

“…The stiffening of the solid in these samples can not be attributed to the pinning of dislocation lines by 3 He impurities. It has been shown recently [37] that the onset of superfluidity in and around the cores of dislocation lines can lead to an increase of the shear modulus of the solid by decreasing the mobility of the dislocation lines. Quantum Monte Carlo calculations [38][39][40] have shown that superfluidity can occur in the vicinity of structural defects such as dislocations and grain boundaries in solid 4 He.…”