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

## TL;DR

This paper revisits the effects of anisotropic shear stress on Sr$_2$RuO$_4$, clarifies elastic theoretical frameworks, and provides experimental evidence supporting a two-component superconducting order parameter with broken time-reversal symmetry.

## Contribution

It offers a detailed analysis of shear stress effects in Sr$_2$RuO$_4$, clarifies elastic theory for sound speed experiments, and presents evidence for a two-component order parameter with broken time-reversal symmetry.

## Key findings

- Discontinuity in elastic constant C$_{xyxy}$ indicates a two-component superconducting order parameter.
- Elastic theoretical framework clarifies interpretation of sound speed and strain experiments.
- Coupling of the $ ext{γ}$ band to in-plane shear stress supports anisotropic electron-phonon interaction model.

## 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].