Supercurrent carried by nonequilibrium quasiparticles in a multiterminal Josephson junction

We theoretically study coherent multiple Andreev reflections in a biased three-terminal Josephson junction. We demonstrate that the direct current flowing through the junction consists of supercurrent components when the bias voltages are commensurate. This dissipationless current depends on the phase in the superconducting leads and stems from the Cooper pair transfer processes induced by nonlocal Andreev reflections of the quasiparticles originating from the superconducting leads. We identify supercurrent-enhanced lines in the current and conductance maps of the recent measurement [PNAS 115, 6991 (2018)] on a nanowire Josephson junction and show that the magnitude of the phase-dependent current components is proportional to the junction transparency with the power corresponding to the component order.

Figure 1

Schematics of the considered device with three semi-infinite superconducting leads (blue) and normal scattering region (gray).

Figure 2

(a) dc current in the first lead for $D=0.5$. (b) Differential conductance obtained from the map of (a).

Figure 3

dc current (solid and dotted curves) in the leads vs the bias energy $eV$ with $V_2=V_3=V$ and $D=0.5$. Dashed curves present dc components $I_{ı,j}^I$ of the current in the first lead. $G_T=e^{2}D/\pi \hslash$. (b) Cross section of the current map of Fig. 2 for $e{V}_3=0.7\mathrm{\Delta }$.

Figure 4

(a) dc current running between the second and the third lead $I^{\text{II}}-I^{\text{III}}$ for three values of the central region transparency $D$ for $V_2=V_3=e\mathrm{\Delta }/2$ vs the phase on the second lead. (b) Components of the current for $D=0.75$.

Figure 5

Same as Fig. 4 but for $V_2=-V_3=e\mathrm{\Delta }/2$.

Figure 6

$I^{\text{II}}-I^{\text{III}}$ dc current component $ı=-j=2$ calculated for different source terms $(s$ – the source position, $p$ – quasiparticle type).

Figure 7

Probabilities of the wave-function components adjacent to the second lead for electronlike quasiparticle as the source term at energy $-1.0001\mathrm{\Delta }$ injected from the first lead. Transparency is $D=0.75$ and $e{V}_2=e{V}_3=\mathrm{\Delta }/2$. The insets on the right-hand side show two scattering processes contributing to the second dc component (quasiparticle-induced supercurrent) that result from an electron (red filled circle) propagating towards the scattering region.

Figure 8

Critical current between second and third lead vs the junction transparency $D$ for $e{V}_2=e{V}_3=1.4\mathrm{\Delta }$ (a) and $e{V}_2=-e{V}_3=1.4\mathrm{\Delta }$ (b). The open circles present the numerical results, and the curves are analytical dependencies as described in the text.

Figure 9

Second derivative of the current in the first lead for $D=0.25$ (a), $D=0.5$ (b), and $D=0.75$ (c). The centrifugal lines are enhanced by the supercurrent.