Emergent spin-resolved electronic density waves from strong $d$-wave altermagnetism and pseudogap phenomena from phason fluctuations

Metallic $d$-wave altermagnets provide a unique setting in which strong spin-momentum locking can qualitatively reshape electronic instabilities. Here we develop a self-consistent microscopic theory beyond the mean-field approximation for density-wave order in $d$-wave altermagnetic metals. The altermagnetic band structure with strong spin-momentum locking reconstructs the Fermi surface into mutually orthogonal spin-selective quasi-1D sectors, whose strong nesting drives density-wave instabilities in the respective spin sectors. The resulting spin-resolved density-wave orders nevertheless share a common ordering wave vector and give rise to a distinct class of stripe states, accompanied by pronounced gap openings on the nested Fermi sheets. The relative phase between the two spin sectors controls the character of the collective order, allowing charge density wave, spin density wave, and mixed density-wave orders to emerge within the same ordered manifold. As temperature increases from zero, thermal excitation of the emergent phason mode induces strong phase fluctuations that destroy long-range density-wave order at $T_c$, while the single-particle gap remains finite, giving rise to a robust pseudogap regime that persists up to a higher temperature $T_g$. The theory reveals a density-wave mechanism unique to metallic $d$-wave altermagnets, rooted in strong spin-selective Fermi-surface reconstruction, and establishes a fluctuation-driven route to pseudogap phenomena governed by phason dynamics. Applied to the metallic $d$-wave altermagnet KV$_2$Se$_2$O, our simulations quantitatively reproduce the key spectroscopic features reported in recent experiments, providing a unified microscopic understanding of the underlying phenomena.