Superconducting States and Fluctuation-Induced Intertwined Orders in Metallic Altermagnets

Altermagnets are a newly identified class of magnets with nodal spin-split band structures, providing a fertile platform for studying unconventional superconductivity and intertwined orders. We investigate multicomponent superconductivity and fluctuation-induced intertwined orders in a d-wave metallic altermagnet. Within mean-field theory, the ground state is a $p_x \pm i p_y$ superconductor with unequal amplitudes of the $p_x$ and $p_y$ components in the two spin-polarized Fermi surfaces related by $C_4T$ symmetry. Distinct fluctuations of sub-leading normal-state instabilities lead to qualitatively different behaviors: nematic fluctuations enhance competition between superconducting components and stabilize a rich phase diagram with nematic superconducting phases, whereas current-loop fluctuations promote coexistence and select a pair of chiral states, lifting the ground-state degeneracy. Our results uncover the pairing structure and elucidate how subleading fluctuations shape superconducting order in altermagnetic metals, suggesting a route toward realizing nematic and topological superconductivity.