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Interfacial spin-orbit coupling in superconducting hybrid systems

A. A. Mazanik1,*, Tim Kokkeler2,3,†, I. V. Tokatly2,4,5,‡, and F. Sebastian Bergeret1,2,§

  • *Contact author: andrei.mazanik@csic.es
  • †Contact author: tim.kokkeler@dipc.org
  • ‡Contact author: ilya.tokatly@ehu.es
  • §Contact author: fs.bergeret@csic.es
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Phys. Rev. B 112, 024514 – Published 28 July, 2025

DOI: https://doi.org/10.1103/dsxt-phyk

Abstract

We investigate the effects of interfacial spin-orbit coupling (ISOC) on superconductors, focusing on its impact on electronic transport and spin-charge conversion. Using a symmetry-based nonlinear sigma model, we derive effective boundary conditions for the Usadel and Maxwell equations that account for the spin-galvanic effect, spin relaxation, and spin precession. This approach allows for the analysis of various interfaces without relying on specific microscopic models. We apply these boundary conditions to derive ISOC-induced terms in the Ginzburg-Landau functional, which is then used to compute the critical temperature of superconducting films with ISOC subjected to an external magnetic field. Our findings show that, contrary to a recent prediction, the critical temperature of a film cannot be enhanced by an external magnetic field. Additionally, we demonstrate that the combination of ISOC and an external magnetic field leads to a superconducting-diode effect. Its efficiency strongly depends on the interplay between the spin-galvanic and the spin relaxation terms. Our results provide a framework for understanding ISOC in superconducting systems and highlight the potential for optimizing diode efficiency through careful interface engineering.

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Phys. Rev. B 112, 024514– Published 28 July, 2025
  • Received 21 February 2025
  • Revised 15 May 2025
  • Accepted 2 July 2025
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