Theory of superconducting SF and SFS junctions in the clean limit for temperatures $T\ll T_C$

S. V. Kuplevakhskii ; I. I. Fal'ko

Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 2, pp. 272-284

Résumé

The semiclassical equations of the theory of superconductivity are solved for superconductor-ferromagnetic-metal and superconductor-ferromagneticmetal-superconductor junctions. It is shown that the superconducting correlations cannot penetrate into the ferromagnetic film to distances greater than a certain critical value $z_C$. As for $T\lesssim T_C$, $z_C=\beta_h v_0/h$, $(h/E_F)^{1/2}\beta_h\leqslant 0{,}79$, where $v_0$ is the Fermi velocity, $h$ is the parameter of the exchange interaction, and $E_F$ is the Fermi energy. The excitation spectrum is obtained in the barrier region (for SFS junction if the thickness $d$ of the ferromagnetic barrier is less than the critical value $d_C\propto z_C$), and the possible existence of singular polarized states of the Andreev quasiparticle is predicted. For weak exchange fields ($h\ll T$ for $T>0$ and $h\ll T_C$ for $T=0$) and broad SFS junctions ($\xi(T)\equiv v_0/2\pi T\ll d$ for $T>0$, $\xi_0\equiv v_0/2\pi T_C\ll d$ for $T=0$) a theory of the Josephson effect is constructed. At $T=0$, the current-phase dependence is nontrivial.