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More than two decades after the discovery of superconductivity inSr$_2$RuO$_4$, it is still unclear whether the order parameter has a singlecomponent or two degenerate components. For any two-component scenario,application of uniaxial strain is expected to lift the degeneracy, generatingtwo distinct phase transitions. The presence of a second (lower-temperature)transition may be observable by probes that are sensitive to changes in theLondon penetration depth, $\lambda$, as a function of temperature, $T$. Here,we use scanning SQUID microscopy combined with a uniaxial strain device to testfor a second transition under strain. We only observe a single transition.Within the temperature range where a second transition has been suggested by$\mu$SR measurements, we further place a tight upper bound of less than 1% onthe change in the zero temperature superfluid density$n_s\propto\lambda^{-2}(0)$ due to a second transition, suggesting that such atransition does not occur. These results constrain theories of the orderparameter in Sr$_2$RuO$_4$.

Constraints on a split superconducting transition under uniaxial strain in Sr$_2$RuO$_4$ from scanning SQUID microscopy