We present an analytical study of the ground-state phase diagram for dilute two-dimensional spin-$\frac{1}{2}$ Fermi gases exhibiting $d$-wave altermagnetic spin splitting under $s$-wave pairing. Within the Bogoliubov–de Gennes mean-field framework, four distinct phases are identified: a Bardeen-Schrieffer-Cooper type superfluid, a normal metallic phase, a nodal superfluid with topological Bogoliubov Fermi surfaces (TBFSs), and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states with finite center-of-mass momentum. Among these, the FFLO states and TBFSs exemplify two unconventional forms of superconductivity. Considering the simplicity of this model, with only one band, zero net magnetization, and $s$-wave paring, the emergence of both unconventional phases underscores the pivotal role of altermagnetic spin splitting in enabling exotic pairing phenomena. This analytical study not only offers a valuable benchmark for future numerical simulations, but also provides a concrete experimental roadmap for realizing FFLO states and TBFSs in altermagnets.

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• Altermagnetism
• FFLO
• Phase diagrams
• 2-dimensional systems
• Altermagnets
• Superconductors
• Bogoliubov-de Gennes equations