Constraints on a split superconducting transition under uniaxial strain in Sr₂RuO₄ from scanning SQUID microscopy

More than two decades after the discovery of superconductivity in Sr₂RuO₄, it is still unclear whether the order parameter has a single component or two degenerate components. For any two-component scenario, application of uniaxial strain is expected to lift the degeneracy, generating two distinct phase transitions. The presence of a second (lower-temperature) transition may be observable by probes that are sensitive to changes in the London penetration depth, λ, as a function of temperature, T . Here, we use scanning SQUID microscopy combined with a uniaxial strain device to test for a second transition under strain. We only observe a single transition. Within the temperature range where a second transition has been suggested by μSR measurements [Grinenko et al., Nat. Phys. 17, 748 (2021)], we further place a tight upper bound of less than 1% on the change in the zero temperature superfluid density n_s ∝ λ^-2(0) due to a second transition, suggesting that such a transition does not occur. These results constrain theories of the order parameter in Sr₂RuO₄.