Metallic altermagnets are unusual collinear magnets that feature zero net magnetization with momentum-dependent spin splitting. Here, we show that this spin splitting can induce pair density wave states even in the absence of external magnetic fields. Focusing on BCS-type attractive interactions, we find the stabilization of symmetrically distinct pair density wave states depending on the chemical potential. These states include Fulde-Ferrell and Fulde-Ferrell* states, both of which break inversion symmetry. We investigate the supercurrent properties and discover nonreciprocal supercurrents for both the Fulde-Ferrell and Fulde-Ferrell* states with distinct spatial dependencies. We propose that the supercurrent diode effect can serve as an experimental tool for distinguishing between different pair density waves in metallic altermagnets and discuss the relation to material candidates.

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• Josephson effect
• Pair density wave
• Altermagnets
• Superconductivity
• Landau-Ginzburg theory