Quartet currents in a biased three-terminal diffusive Josephson junction

TL;DR

This paper investigates the novel quartet Josephson currents in a biased three-terminal diffusive Josephson junction, analyzing their dependence on phase, voltage, transparency, and decoherence, and distinguishing them from multiple Andreev reflection currents.

Contribution

It introduces a comprehensive quantum circuit theory analysis of quartet currents in a three-terminal Josephson junction, including effects of decoherence and asymmetry, with analytic expressions in certain regimes.

Findings

Quartet currents exhibit sign changes influenced by voltage, transparency, and decoherence.

Analytic perturbative formulas agree well with numerical results in low transparency, asymmetric regimes.

Distinct regimes allow separation of quartet and MAR currents based on parameters.

Abstract

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 $\varphi_Q=\varphi_1+\varphi_2-2\varphi_0$ of the terminal phases $\varphi_i$, 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 an "funnel" regime with very asymmetric couplings to $S_{0,1,2}$. In the regime of low transparency and asymetric couplings, we provide an analytic perturbative expression for the currents which shows an excellent agreement with the full numerical results.