Biasing a three-terminal Josephson junction (TTJ) with symmetrical voltages $0,V,-V$ leads to new kinds of DC currents, namely quartet Josephson currents and phase-dependent multiple Andreev reflection (MAR) currents. We study these currents in a system where a normal diffusive metallic node $N$ is connected to three terminals $S_{0,1,2}$ by barriers of arbitrary transparency. We use the quantum circuit theory to calculate the current in each terminal, including decoherence. In addition to the stationary combination ${\phi }_Q={\phi }_1+{\phi }_2-2{\phi }_0$ of the terminal phases ${\phi }_i$, the bias voltage $V$ appears as a new and unusual control variable for a DC Josephson current. A general feature is the sign changes of the current-phase characteristics, manifesting in minima of the quartet “critical current”. Those sign changes can be triggered by the voltage, by the junction transparency or by decoherence. We study the possible separation of quartet currents from MAR currents in different regimes of parameters, including a “funnel” regime with very asymmetric couplings to $S_{0,1,2}$. In the regime of low transparency and asymmetric couplings, we provide an analytic perturbative expression for the currents, which shows an excellent agreement with the full numerical results.

• Received 13 July 2023
• Revised 14 November 2023
• Accepted 15 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.214517