Anisotropic shear stress $\sigma_{xy}$ effects in the basal plane of Sr$_2$RuO$_4$

Abstract

In this short note, we repeat the calculations the jumps for the specific heat C$_{\sigma_{xy}}$, the elastic compliance S$_{xyxy}^{\sigma_{xy}}$ and the thermal expansion $\alpha_{\sigma_{xy}}$ due to a shear stress $\sigma_{xy}$ in the basal plane of $Sr_2RuO_4$. Henceforth we clarify some issues regarding the elastic theoretical framework suitable to explain the sound speed experiments of Lupien et al. (2001,2002), and partially the strain experiments of Hicks et al. (2014), and Steppke et al. (2016) in strontium ruthenate. We continue to propose that the discontinuity in the elastic constant C$_{xyxy}$ of this tetragonal crystal gives unambiguous experimental evidence that the superconducting order parameter $\Psi$ has two components with a broken time-reversal symmetry state, and that the $\gamma$ band couples the anisotropic electron-phonon interaction to the $[xy]$ in-plane shear stress according to Walker and collaborators [4] and [3]. Some importants words about the roll of the spin equal to one for the transversal phonons are added in the conclusion following Levine [34].