Micron-scale measurements of low anisotropic strain response of local $T_c$ in Sr${}_2$RuO${}_4$

Abstract

Strontium ruthenate (Sr${}_2$RuO${}_4$) is a multiband superconductor that displays evidence of topological superconductivity, although a model of the order parameter that is consistent with all experiments remains elusive. We integrated a piezoelectric-based strain apparatus with a scanning superconducting quantum interference device (SQUID) microscope to map the diamagnetic response of single-crystal Sr${}_2$RuO${}_4$ as a function of temperature, uniaxial pressure, and position with micron-scale spatial resolution. We thereby obtained local measurements of the superconducting transition temperature $T_c$ vs. anisotropic strain $\epsilon$ with sufficient sensitivity for comparison to theoretical models that assume a uniform $p_x\pm i{p}_y$ order parameter. We found that $T_c$ varies with position and that the locally measured $T_c$ vs. $\epsilon$ curves are quadratic ($T_c\propto {\epsilon }^2$), as allowed by the C${}_4$ symmetry of the crystal lattice. We did not observe the low-strain linear cusp ($T_c\propto \left|\epsilon \right|$) that would be expected for a two-component order parameter such as $p_x\pm i{p}_y$. These results provide new input for models of the order parameter of Sr${}_2$RuO${}_4$.

18 pages, 6 figures, 2 tables