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Dislocation Mobility and Anomalous Shear Modulus Effect in \(^4\)He Crystals

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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.

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Notes

  1. The first of Eqs. (8) differs slightly from the corresponding expression in the first of Ref. [33, 34]. That expression contains a small error, which we are very grateful to Prof. Saslow for pointing out to us.

  2. We consider the limit whereby the effective mass per unit length as well as the effective tension per unit length of the dislocation line is negligible.

  3. The acceleration time constant is given by the ratio of mass per unit length to the inverse mobility of the dislocation line. This time constant is very small \(\sim 10^{-13}\) s.

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Acknowledgments

This research was supported in part by IUSSTF Grant 94-2010.

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Author notes

  1. Abdul N. Malmi-Kakkada

    Present address: Department of Chemistry, University of Texas at Austin, 105 E 24th St, Austin, TX, 78712, USA

Authors and Affiliations

  1. School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, 55455, USA

    Abdul N. Malmi-Kakkada & Oriol T. Valls

  2. Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, 560012, India

    Chandan Dasgupta

Authors
  1. Abdul N. Malmi-Kakkada
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  2. Oriol T. Valls
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  3. Chandan Dasgupta
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Correspondence to Oriol T. Valls.

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Malmi-Kakkada, A.N., Valls, O.T. & Dasgupta, C. Dislocation Mobility and Anomalous Shear Modulus Effect in \(^4\)He Crystals. J Low Temp Phys 186, 259–274 (2017). https://doi.org/10.1007/s10909-016-1689-3

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