Real devices are rarely perfectly clean or completely disordered. This theory describes the Josephson current in superconductor–normal metal–superconductor junctions with spin-dependent fields, such as spin–orbit coupling, Zeeman fields and altermagnetism, at any disorder strength, beyond the usual ballistic and diffusive approximations.

The authors show how the critical current in a magnetic field can probe spin–orbit coupling, that the anomalous (φ₀) Josephson effect stays robust over a wide range of disorder and can even be enhanced by moderate disorder, and that disorder suppresses the 0–π transition in altermagnetic junctions. The work is by Maryam Darvishi and Stefan Ilić of QMAT's Condensed Matter Theory group at the University of Jyväskylä, with Sebastián Bergeret in San Sebastián.

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