Elastic constants and supersolidity in solid hcp 4He

Abstract

The elastic constants of solid hcp 4 He are investigated in molar volumes ranging from about melting up to approximately 14 MPa. Properties of interest are determined by averages formed from computed values in configurations sampled by Monte Carlo of a model wave function. Deviations from known elastic relations are reported near the density where the supersolid fraction is maximum. The results offer further evidence that the supersolid state is related to elastic constants anomalies and that both are manifestations of a single physical process.1 For more than a hundred years, since it has been liquefied, helium has shown intriguing behaviors and has provided invaluable clues for the condensed matter physics. Nowadays, despite a reasonable good understanding of its liquid phase, solid helium is still revealing fascinating aspects that defy experimentalists and theoreticians. The shear modulus softening with temperature increase, as observed by Day and Beamish[1], and its connections to supersolidity, superfluidity superimposed to crystalline order, as seen in the pioneering experiments by Kim and Chan[2, 3] illustrate very well this situation.Elasticity is ubiquitous among materials and has been extensively investigated in solids where atomic exchange is negligible, and the atoms are reasonable localized and distinguishable. If forces that are not too strong are applied in the surfaces of these solids, they will produce mechanical deformations that will increase the potential energy. As the solid is released from these forces and assuming they are small enough, it will go back to its original state. However, what can be said about quantum solids? Systems where the zero-point kinetic energy is comparable to the binding energy of the atoms that perform large excursions from their mean positions in the lattice. How will these quantum systems respond to applied forces?This letter reports values of all the five independent elastic constants, as a function of the density, which characterize a defect-free single crystal of 4 He in an hcp structure. We have analyzed our results using relations among the elastic constants that are satisfied under well defined conditions. Since all the elastic constants were determined, it was possible to some extent verify the internal consistence of our calculations and search for elastic anomalies in this quantum solid. In fact, we have observed deviations of the relations occurring near the same density where the mass decoupling in the movement of torsional oscillators has its maximum. [4] In our view these results are further evidences that supesolidity[2, 3] and elastic anomalies [1,5] of the shear modulus are related phenomena and consequence of a single physical process.The elastic constants were calculated at zero temperature using a model wave function that has allowed an excellent description of various properties of 4 He in both the liquid and solid phases. [6,7] It is worth mentioning that the interacting potential for the helium atoms is very accurately known as more than one...