Magnetic Quantum Criticality inside the Superconducting State Revealed by Penetration Depth Scaling with Local $T_{\mathrm{c}}$

Abstract

We demonstrate a magnetic quantum critical point embedded within the superconducting state of Zn-doped CeCoIn${}_5$, revealed by a pronounced peak in the magnetic penetration depth at zero temperature $\lambda (0)$. Using scanning SQUID microscopy, we determine the local superconducting transition temperature $T_{\mathrm{c}}$ and $\lambda (0)$. By parameterizing $\lambda (0)$ in terms of the local $T_{\mathrm{c}}$ rather than nominal Zn substitution, we circumvent the ambiguity caused by doping inhomogeneity and enable a more precise extraction of the critical exponent. The extracted exponent exceeds the clean spin-density-wave value, indicating a disorder-modified quantum critical regime. The enhancement of $\lambda (0)$ reflects the suppression of the superfluid stiffness and is consistent with critical scaling. Our approach provides a route to uncover intrinsic quantum critical behavior hidden by inhomogeneity in unconventional superconductors.

11 pages, 9 figures