Phonon-mediated spin-polarized superconductivity in altermagnets

We consider the possibility of phonon-mediated unconventional superconductivity in a recently discovered new class of antiferromagnets, dubbed altermagnets. Within a weak-coupling approach, and using a minimal Lieb lattice model for altermagnets, we find a dominant superconducting instability odd in momentum and even in spin with spin-polarized Cooper pairs. We discuss the origin of this unusual result in terms of the spin-structure of the altermagnetic Fermi surface, in combination with the momentum-space structure of the effective phonon-mediated electron-electron interactions on the Fermi surface.