Proximity effect in ballistic superconductor-ferromagnet structures with spin-orbit coupling
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- Institutt for fysikk 
The Bogoliubov-de Gennes equations have been solved numerically for a number of two-dimensional ballistic proximity structures comprised of superconductors, normal metals and ferromagnets, with both interfacial and in-plane spin-orbit coupling. These results have been compared to results obtained for similar structures in the absence of spin-orbit coupling. The results show that spin-orbit coupling in general enhances superconductivity in ferromagnet-superconductor-structures, and causes the critical temperature, as well as singlet and triplet amplitudes, to become dependent upon the orientation of the magnetic field. The protective effect of spin-orbit coupling on the superconducting state grows stronger the closer the magnetic field comes to being perpendicular to the effective fields induced by spin-orbit coupling. Both interfacial and in-plane spin-orbit coupling have these effects in common, but the effect is most prominent for the in-plane spin-orbit coupling. The observed effects can be explained by projecting the Cooper pair states onto the eigenbasis of the system, which reveals that the singlet state adapts a long-ranged pseudotriplet component in the presence of spin-orbit coupling. Spin-orbit coupling thus serves as an alternative to inhomogeneously magnetized structures, as it enables control of the critical temperature, as well as both singlet and triplet amplitudes, by adjusting macroscopic parameters. Additionally, the protective effect spin-orbit coupling introduces on the superconducting state allows for such structures to be made smaller than in its absence.