Electronic structure of pairing states in d-wave altermagnetic Fermi gases: from a conventional BCS superfluid to unconventional superfluids

We systematically investigate the pairing-state electronic structure of two-dimensional d-wave altermagnetic Fermi superfluid gases under an applied Zeeman field. By calculating the spectral function, we obtain the Fermi surface, dispersion, and density of states (DOS), and further analyze the main characteristics of different superfluid phases, particularly the polarized BCS (PBCS) state and two kinds of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states: the altermagnetism-driven FFLO (AFFLO) and the Zeeman-field-induced FFLO (ZFFLO) states. The Bogoliubov Fermi surface (BG-FS) emerges in these unconventional phases, giving rise to gapless Bogoliubov quasiparticles. A Lifshitz transition occurs when the system undergoes a phase transition between these exotic phases. In the PBCS state, two Fermi pockets appear, and their size is proportional to the Zeeman field strength. The Fermi surface in the AFFLO state exhibits the coexistence of the Fermi arcs and Fermi pockets, while in the ZFFLO state, two large crescent-shaped Fermi pockets overlap. Our results not only play a significant role in understanding the interplay between the d-wave altermagnetism and s-wave contact interaction, but also provide crucial guidance for the experimental search and study of these exotic superfluid states. Moreover, the electronic structure can be directly measured via angle-resolved photoemission spectroscopy (ARPES).