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

We explore the possibilities for spin-singlet superconductivity in newly discovered altermagnets. Investigating <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>d</a:mi></a:math>-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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>d</b:mi></b:math>-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.