Enhancement of superconductivity by polarization of magnetic impurities in disordered films

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 $λL$ 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 $λ_L$ and the enhancement of $H{c2}^{\perp}$ by a parallel magnetic field, in agreement with experiment.