Enhancement of superconductivity by polarization of magnetic impurities in disordered films

TL;DR

This paper develops a theoretical framework extending KF theory to explain how magnetic fields can enhance superconductivity and related properties in disordered films with magnetic impurities, aligning with recent experimental observations.

Contribution

It introduces an extended Gor'kov diagrammatic approach to analyze multiple superconducting observables under various magnetic field orientations at arbitrary temperatures.

Findings

Parallel magnetic field suppresses London penetration depth λ_L.

Parallel magnetic field enhances perpendicular upper critical field H_{c2}^{ot}.

Theory aligns with recent experimental results.

Abstract

Dirty superconducting films with magnetic impurities can exhibit nontrivial behavior in a magnetic field that polarizes the impurity spins. As predicted by Kharitonov and Feigelman (KF) [JETP Lett. 82, 421 (2005)], this polarization reduces the exchange scattering rate. Consequently, a parallel magnetic field can enhance the critical temperature $T_c$ when magnetic-field pair breaking is weak, as realized for strong spin-orbit scattering and small film thickness. Recently, Llanos et al. [Nat. Phys. (2026)] observed a pronounced enhancement of $T_c$ consistent with the KF theory. The same experiment also reported an enhancement of the perpendicular upper critical field $H_{c2}^{\perp}$ and a suppression of the London penetration depth $\lambda_L$ by a parallel magnetic field. These quantities were not considered in the original KF theory. To address this gap, we develop a theoretical framework based on Gor'kov's diagrammatic technique for dirty superconductors. We extend the KF theory in two experimentally relevant directions: (i) to arbitrary temperatures $T<T_c$ and several superconducting observables, and (ii) to arbitrary magnetic-field orientations. As a result, we demonstrate theoretically the suppression of $\lambda_L$ and the enhancement of $H_{c2}^{\perp}$ by a parallel magnetic field, in agreement with experiment.