Stimulated by recent interest in altermagnets, a novel class of antiferromagnets with macroscopic time-reversal symmetry breaking, we investigate the coexistence of altermagnetism and superconductivity. By developing a Ginzburg-Landau theory based on microscopic models, we show that a phase-modulated Fulde-Ferrell superconducting state is stabilized via altermagnetic spin splitting, in contrast to the typical amplitude-modulated states that occur under the uniform Zeeman field. We apply our framework to different models to compare the resulting phase diagrams: a two-sublattice model with altermagnetic order, a continuum model with an anisotropic Zeeman field mimicking altermagnetic spin splitting, and a conventional square-lattice model with two kinds of anisotropic Zeeman fields. We show that the multisublattice structure is crucial for realizing the phase-modulated superconductivity, and highlight spin-split altermagnets as a promising platform for exploring this exotic superconductivity without external magnetic fields.

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• FFLO
• Superconductivity
• Altermagnets
• Unconventional superconductors
• Eliashberg theory
• Landau-Ginzburg theory