φ Josephson Junction Induced by Altermagnetism

We study the Josephson effect in a superconductor-altermagnet-superconductor junction. We find anomalous phenomena, including 0-π transition and multinodal current-phase relations. Similar to a d-wave superconductor, a d-wave altermagnet can support a φ junction where free-energy minima locate neither φ=0 nor ±π with double degeneracy. These properties can be tunable by parameters, e.g., the exchange energy, the orientation of crystal axis, the length, and the chemical doping of the altermagnet. These rich features lead to accessible functionality of superconductor-altermagnet-superconductor junctions.