T$_c$ and the elastocaloric effect of Sr$_2$ RuO$_4$ under 〈110〉 uniaxial stress: No indications of transition splitting

There is considerable evidence that the superconductivity of Sr2⁢RuO4 has two components. Among this evidence is a jump in the shear elastic modulus 𝑐66 at the critical temperature 𝑇𝑐, observed in ultrasound measurements. Such a jump is forbidden for homogeneous single-component order parameters, and it implies that 𝑇𝑐 should develop as a cusp under the application of shear strain with ⟨110⟩ principal axes. This shear strain should split the onset temperatures of the two components, if they coexist, or select one component if they do not. Here, we report measurements of 𝑇𝑐 and the elastocaloric effect of Sr2⁢RuO4 under uniaxial stress applied along the [110] lattice direction. Within experimental resolution, we resolve neither a cusp in the stress dependence of 𝑇𝑐, nor any second transition in the elastocaloric effect data. We show that reconciling these null results with the observed jumps in 𝑐66 requires extraordinarily fine tuning to a triple point of the Ginzburg-Landau parameter space. In addition, our results are inconsistent with homogeneous time-reversal symmetry breaking at a temperature 𝑇2≤𝑇𝑐 as identified in muon spin relaxation experiments.