We investigate the superconducting instabilities induced by altermagnetic fluctuations. Because of the nontrivial sublattice structure of the altermagnetic order, shorter-range and longer-range fluctuations favor qualitatively different types of pairing states. Specifically, while the latter stabilize a standard spin-triplet $p$-wave state, just like ferromagnetic fluctuations, the former leads to intra-unit-cell pairing, in which the Cooper pairs are formed by electrons from different sublattices. The symmetry of the intra-unit-cell gap function can be not only $p$-wave, but also spin-singlet $s$-wave and $d$-wave, depending on the shape of the Fermi surface. We also show that coexistence with altermagnetic order promotes intrinsic nontrivial topology, such as protected Bogoliubov Fermi surfaces and higher-order topological superconductivity. Our Letter establishes the key role played by sublattice degrees of freedom in altermagnetic-fluctuation mediated interactions.

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• Spin fluctuations
• Superconductivity
• Topological superconductors
• Altermagnets