Anomalous Josephson current through a spin-orbit coupled quantum dot

For a general model of a mesoscopic multi-level quantum dot, we determine the necessary conditions for the existence of an anomalous Josephson current with spontaneously broken time-reversal symmetry. They correspond to a finite spin-orbit coupling, a suitably oriented Zeeman field, and the dot being a chiral conductor. We provide analytical expressions for the anomalous supercurrent covering a wide parameter regime.