Altermagnetism-induced Fulde-Ferrell-Larkin-Ovchinnikov superfluids and momentum-selective pairing channels in optical lattices
We study the superfluid phases of a two-dimensional degenerate Fermi gas in an optical lattice subject to a $d_{xy}$-wave altermagnetic term that couples to the in-plane spin component. The single-particle Hamiltonian generates anisotropic Fermi surfaces for the two pseudo-spin species while maintaining zero net polarization. Using the Bogoliubov-de Gennes approach, we show that this anisotropy favors Cooper pairing at a finite center-of-mass momentum, producing a competition between Bardeen-Cooper-Schrieffer (BCS) and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing and leading to FFLO superfluids. We further examine the effect of a Zeeman-induced spin polarization and find that triplet and singlet pairing channels coexist and compete, resulting in a momentum-selective pairing pattern. Remarkably, this triplet pairing emerges exclusively in the FFLO phase and is entirely absent in the BCS phase. The model is readily realizable in ultracold atoms with current experimental techniques, providing a feasible route for quantum emulation and for studying unconventional superfluid phases.