Theory of superconductivity enhancement due to polarization of magnetic impurities in dirty films

Thin dirty superconducting films containing magnetic impurities can exhibit nontrivial behavior when subjected to an applied magnetic field. This behavior manifests itself in the enhancement of superconductivity, which is related to the reduction in the exchange scattering rate due to the polarization of the impurity spins in the presence of the magnetic field. This mechanism of superconductivity enhancement was theoretically predicted by Kharitonov and Feigelman many years ago [JETP Lett. 82, 421 (2005)]. However, in their study the authors concentrated only on the dependence of the critical temperature T_c on the magnetic field parallel to the film surface H_{par}, revealing a nonmonotonic behavior characterized by a maximum at finite field values. At the same time, it is also of interest to investigate other manifestations of this enhancement. Moreover, recent experiments require theory describing the effect at lower temperatures and in the presence of a magnetic field component perpendicular to the film surface H_{perp}. Therefore, to address this gap, we develop a theoretical framework employing Gor’kov diagrammatic technique for dirty superconductors. Our work extends the theory by Kharitonov and Feigelman in two directions: (i) we generalize the theory to arbitrary temperatures T < T_c and demonstrate a nonmonotonic behavior of the superfluid density as a function of H_{par}, (ii) we reveal a nonmonotonic dependence of the second critical field (perpendicular to the film surface) on the magnetic field component parallel to the surface, H_{c2}(H_{par}) dependence.