Influence of elastic deformations on the supersolid transition

Abstract

We study within the Ginzburg-Landau (GL) theory of phase transitions how elastic deformations in a supersolid lead to local changes in the supersolid transition temperature. The GL theory is mapped onto a Schrödinger-type equation with an effective potential that depends on local dilatory strain. The effective potential is attractive for local contraction and repulsive for local expansion. Different types of elastic deformations are studied. We find that a contraction (expansion) of the medium that may be brought about by either externally applied or internal strain leads to a higher (lower) transition temperature as compared to the unstrained medium. In addition, we investigate edge dislocations and illustrate that the local transition temperature may be increased in the immediate vicinity of the dislocation core. Our analysis is not limited to supersolidity. Similar strain effects should also play a role in superconductors.

Defects and Glassy Dynamics in Solid 4He: Perspectives and Current Status

“…Similar effects are at play in the quantum arena where mobile dislocations (dislocation currents) lead to a screening of applied shear via a Meissner-Higgs type effect [60,61]. Such unpinned dislocations that screen shear render the system more fluid and may, in line with the framework that we advance in this article, trigger the 4 He anomalies as the mobile dislocations become quenched at low temperatures [44,59]. Recent experiments provide further impetus for such a picture [62,63].…”

“…Most of the literature reviewing the subject deals with the notion of supersolidity in 4 He as established and proceeds with the discussion on the status and future experiments with the goal of further "proving" the existence of a supersolid phase transition at very low temperatures. Amongst the many exciting proposals concerning 4 He as well as supersolids, we briefly mention Andreev's proposal for superglass [37,38,39], Anderson's suggestion of vortex proliferation and flow [40,41] and supersolid dislocation cores [42,43,44,45]. As will become evident in later sections, our analysis centers on the dynamical effects of defects and as such may include vortices, dislocations, or any other defects.…”

Phase ordering kinetics of second-phase formation near an edge dislocation

“…This series is asymptotically convergent. In Appendix A, we have given the first three coefficients of the series (21), which are adequate for convergence. Figure 14 depicts √ S/η 0 as a function of the dimensionless time for two values of λ ≡ |r 1 |v 0 /u 2 1 using Eqs.…”

“…Figure 14 depicts √ S/η 0 as a function of the dimensionless time for two values of λ ≡ |r 1 |v 0 /u 2 1 using Eqs. (21) with up to n = 3, and (20) with d = 2. It is seen that an increase in λ slows down the completion of equilibrium.…”

“…Other examples on the effect of dislocations include quantum crystals, metals and semiconductors, in which electrons get localized near an edge dislocation producing discrete levels in certain part of the energy spectrum locally, hence altering the electronic structure of the solid, thereby affecting its thermodynamics and transport properties [16,17]. In a superconductor and a Bose solid, Ginzburg-Landau type model [18] calculations show that superconductive and superfluid phase nucleate first (at higher temperatures) on dislocations prior to the bulk of the crystal [19][20][21].…”