Spin and pair density waves in two-dimensional altermagnetic metals

Altermagnetism, a recently proposed and experimentally confirmed class of magnetic order, features collinear compensated magnetism with unconventional spin-split bands. Here, we show that in a metallic 2D d-wave altermagnet with [C₂||C₄] symmetry, secondary instabilities can arise. Using an unbiased functional renormalization group approach, we analyze the weak-coupling instabilities of a 2D Hubbard model with a preexisting altermagnetic order inspired by our ab initio electronic structure calculations of realistic material candidates from V₂X₂O (X = Te, Se) family. We identify two distinct spin-density-wave (SDW) states that break the underlying altermagnetic [C₂||C₄] symmetry. Additionally, we find spin-fluctuation-induced instabilities leading to a singlet d-wave superconducting state and an unconventional commensurate pair-density-wave (PDW) state with extended s-wave and spin-triplet symmetry. We analyze the pairing mechanism and characterize the excitation spectrum, which exhibits Bogoliubov Fermi surfaces or nodal points depending on the gap size.