Tunable second harmonic in altermagnetic Josephson junctions

We study the influence of external electric and Zeeman fields on the Josephson effect in a planar superconductor/altermagnet/superconductor junction. Remarkably, we find that the current-phase relation (CPR) can be forward or backward skewed due to a pronounced second harmonic term. It decisively depends on the altermagnetic field strength. This second harmonic can be measured directly using double SQUID devices. The CPR skewness can be effectively manipulated by electric gating. Moreover, we identify two additional impacts of external electric and magnetic fields on the Josephson current: (i) Fields can induce 0-$\ensuremath{\pi}$ transitions. (ii) Fields can substantially enhance the critical current. This enhancement is surprising since supercurrents are typically suppressed by magnetic fields.