Emergence of chiral $p$-wave and $d$-wave states in $g$-wave altermagnets

Altermagnets emerge as a novel platform for realizing unconventional superconductivity through their exotic momentum-dependent spin-splitting of electronic band structures. Recent experiments have uncovered a novel form of altermagnetism with distinctive $g$-wave symmetry in CrSb. However, the potential for unconventional superconductivity arising from $g$-wave altermagnetism in such systems remains largely unexplored. In this study, we discover the emergence of chiral superconducting states in three-dimensional $g$-wave altermagnetic metals. Through systematic self-consistent mean-field analysis on the extended attractive Hubbard model combined with $g$-wave altermagnetic exchange fields in a three-dimensional hexagonal lattice, as observed in CrSb, we find that the altermagnetic spin splitting of Fermi surfaces favors chiral $p$-wave states as the dominant pairing channel under strong altermagnetic fields and high electron densities, while chiral $d$-wave states become predominant under weak altermagnetic fields and intermediate electron densities. Conversely, at weak altermagnetic fields and typical electron densities, non-chiral $s$-, extended $s$-, or $f$-wave states become stabilized. We also showcase the possible experimental detection using the quasiparticle energy dispersions and the density of states to distinguish different pairing symmetries. These findings underscore the potential of $g$-wave altermagnets to host sought-after chiral and gapless superconductivity.