Anomalous Josephson effect in altermagnet

\n\nAnomalous Josephson current in an s-wave superconductor junction is due to the parity and time-reversal symmetry breaking from the spin-orbit coupling (SOC) together with magnetization. Altermagnetism is an emerging magnetic phase with the d-wave–type magnetism but zero macroscopic magnetization. Here, we numerically study the Josephson supercurrent in a two-dimensional junction with both the SOC and altermagnetism. It is found that the 0-π transition can appear in the system by modulating the junction's lengths or the SOC strengths despite the zero net magnetization in the system. An anomalous Josephson effect is also identified but dependent on the orientation of magnetization.\n