Magnetic field and flux driven 0-π phase transition in a spinful Josephson junction

The coexistence of magnetism and superconductivity in a Josephson junction can lead to a 0-π phase transition. Quantum dots (QDs) can serve as spin impurities that can be controllably coupled to a superconductor (S). Here, we probe the Andreev spectrum of a hybrid S-QD-S Josephson junction by performing tunneling spectroscopy with a weakly coupled normal lead. We identify a gate-voltage-induced transition from singlet to doublet ground state, where the Andreev spectrum develops a π-phase shift. We demonstrate control of the 0−π transition using superconducting phase difference across the junction and an external magnetic field. We identify parity transitions by measuring zero-bias crossings induced by a magnetic field, phase difference, and gate voltage. This research was supported by Microsoft and the Danish National Research Foundation.