Heat Capacity Measurements of Sr${}_2$RuO${}_4$ Under Uni-axial Stress

We present heat capacity measurements on the superconductor Sr${}_2$RuO${}_4$ under uniaxial stress. Under uniaxial stress, the degeneracy of the components $p_x$ and $p_y$ of the proposed superconducting order parameter $p_x$ $\pm$ $i{p}_y$ should be lifted, resulting in two heat capacity jumps. We have now measured four samples of varying quality, including one where, thanks to high sample quality and careful mounting, the transitions remain very sharp as strain is applied. In measurements up to the peak in Tc (at 3.6 K and a compression of 0.6%), no splitting is observed at any strain. We discuss whether this null result can still be consistent with a hypothesis of $p_x$ $\pm$ $i{p}_y$ superconductivity.