Zero-field finite-momentum and field-induced superconductivity in altermagnets

We explore the possibilities for spin-singlet superconductivity in newly discovered altermagnets. Investigating $d$-wave altermagnets, we show that finite-momentum superconductivity can easily emerge in altermagnets even though they have no net magnetization, when the superconducting order parameter also has $d$-wave symmetry with nodes coinciding with the altermagnet nodes. Additionally, we find a rich phase diagram when both altermagnetism and an external magnetic field are considered, including superconductivity appearing at high magnetic fields from a parent zero-field normal state.