We report on a study of the interplay between the supercurrent and spin-polarization in a two-dimensional superconducting system in the presence of a $d$-wave symmetric antiferromagnetic exchange interaction (altermagnetism). It is demonstrated that the supercurrent exhibits a transverse contribution in the presence of both constant and momentum-dependent exchange interactions. We also discuss the analog of the Edelstein effect for such material, showing that the induced spin polarization is quadratic in the supercurrent and $d$-wave symmetric.

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• Critical current
• Magnetoelectric effect
• Spin polarization
• Spintronics
• Superconductivity
• Unconventional superconductors
• Bogoliubov-de Gennes equations
• Green's function methods
• Landau-Ginzburg theory