Finite-momentum superconductivity with singlet-triplet mixing in an altermagnetic metal: A pairing instability analysis

We analyze the pairing instability of an altermagnetic metal on a square lattice driven by an attractive nearest-neighbor interaction. This interaction enables multiple pairing channels, including even-parity extended $s$-wave and $d$-wave states, as well as two odd-parity $p$-wave channels. We verify that altermagnetic spin-splitting in the single-particle dispersion gives rise to finite-momentum pairing between electrons with unlike spins, in agreement with earlier predictions. Quite unexpectedly, this pairing typically emerges across multiple channels with mixed parity. Consequently, the resulting finite-momentum Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting phase is expected to exhibit a multi-component order parameter featuring singlet-triplet mixing. We examine several forms of altermagnetism, specifically $d_{xy}$-wave and $d_{x^2-y^2}$-wave altermagnetic couplings, and present the corresponding phase diagrams. Additionally, we investigate the triplet pairing between electrons with identical spins, and find that it consistently occurs at zero center-of-mass momentum and is unfavorable at weak altermagnetic coupling and low electron filling. The influence of on-site attractive interactions on mixed-parity pairing is also explored.