Effect of strain inhomogeneity on a chiral $p$-wave superconductor

Motivated by recent measurements of strain effects on the transition temperature ($T_c$) of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, we study the strain response of a two-dimensional chiral $p$-wave superconductor. We focus on the effects of inhomogeneous strain fields, which are always present in any such experiment, and which have been neglected in previous theoretical treatments. We show that the response of $T_c$ of a chiral superconductor to strain changes from being linear without inhomogeneity to being quadratic in the presence of inhomogeneity. We discuss our results in the context of the ongoing debate of superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

Figure 1

Mean-field phase diagram in the absence of disorder. The condition $b_2>0$ and $4b_1-b_2+b_3>0$ is taken such that the chiral $p$-wave state is preferred for $T<T_c^{\left(2\right)}$. Linear phase boundaries are obtained by minimizing the effective energy density Eq. (2). The mean-field solution predicts a kink in the phase boundary at $\varepsilon =0$.

Figure 2

Numerical results for the phase diagrams for (top) $\sigma =0$ and (bottom) $\sigma =0.2$, for weak thermal fluctuation. Phase boundaries $T_c^{\left(1\right)}$ and $T_c^{\left(2\right)}$ are located for seven different average strains $\varepsilon$, using $C=C_{xx}+C_{yy}=\epsilon =0.01$ and $C_{xy}=\epsilon /2=0.005$, respectively. Solid lines are the fitted phase boundary.