Superconductivity induced by altermagnetic spin fluctuations in high-pressure MnB$_4$
Recent experiments found superconductivity in nonmagnetic MnB$_4$ with a high critical temperature ($T_{c}$) reaching 14 K at 158 GPa. However, ab initio calculations of the electron-phonon coupling predict a $T_{c}$ below 1 K, suggesting that a conventional mechanism cannot explain this phenomenon. In this Letter, we find that MnB$_4$ is close to an altermagnetic instability in density-functional theory calculations. We propose that the superconductivity is driven by altermagnetic spin fluctuations. To verify the pairing symmetry, we have constructed a two-orbital tight-binding model, where boron states at the Fermi level are integrated out. Using this model, we identify an extended-$s$ symmetry as the leading pairing instability. If confirmed, this will be the first reported case of superconductivity driven by altermagnetic spin fluctuations.