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

TL;DR

This study used micron-scale measurements to investigate how local superconducting transition temperature $T_c$ in Sr$_2$RuO$_4$ responds to anisotropic strain, revealing a quadratic dependence and challenging some existing models of its order parameter.

Contribution

It provides the first local, high-resolution measurements of $T_c$ versus strain in Sr$_2$RuO$_4$, showing a quadratic response inconsistent with certain two-component order parameter models.

Findings

$T_c$ varies quadratically with strain ($T_c \,\propto\, \epsilon^2$).

No linear cusp in $T_c$ vs. strain was observed.

Results challenge models predicting a linear $T_c$ response for two-component order parameters.

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 $p_x\pm ip_y$ 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 $p_x\pm ip_y$. These results provide new input for models of the order parameter of Sr$_2$RuO$_4$.