Unconventional superconductivity in altermagnets with spin-orbit coupling

Abstract

We investigate some possible symmetries of the superconducting state that emerges in three-dimensional altermagnets in the presence of spin-orbit coupling. We demonstrate within a weak-coupling approach that these altermagnets, which naturally possess an order modulated by a vector form factor gk, favor spin-triplet superconductivity described by gap functions given by d(k)=u(k)×gk, where u(k)=−u(−k). Consequently, this singles out f-wave spin-triplet superconductivity as the most favorable pairing state to appear in the vicinity of d-wave altermagnetism. Furthermore, we obtain that the combination of spin-singlet superconducting states with altermagnetism gives rise to Bogoliubov-Fermi surfaces, which are protected by a Z2 topological invariant. Using a Ginzburg-Landau analysis, we show that, for a class of spin-orbit coupled altermagnetic models, a superconducting phase is expected to appear at low temperatures as an intertwined d+if state, thus breaking time-reversal symmetry spontaneously.

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