Supercurrents in Unidirectional Channels Originate from Information Transfer in the Opposite Direction: A Theoretical Prediction

It has been thought that the long chiral edge channels cannot support any supercurrent between the superconducting electrodes. We show theoretically that the supercurrent can be mediated by a nonlocal interaction that facilitates a long-distance information transfer in the direction opposite of electron flow. We compute the supercurrent for several interaction models, including that of an external circuit.

Figure 1

(a) The basic setup: two superconducting leads biased at phase difference $\varphi ={\varphi }_2-{\varphi }_1$ are attached to the edge of a QH sample. (b) The lowest-order anomalous Green’s function. (c) The noninteracting lowest-order contribution shown vanishes for chiral channels.

Figure 2

Nonvanishing contribution to the superconducting current. The wavy line represents interaction. By virtue of chirality, the points $x$, $x^{\prime }$ are on opposite sides of both $x_1$ and $x_2$. This is only possible if $x^{\prime }<x_1<x_2<x$ and $\omega$ and $\nu$ are of opposite signs.

Figure 3

The QH edge with superconducting contacts included into an external circuit characterized by (frequency-dependent) impedances $Z_{A,B}$. The superconducting current between the terminals 1,2 is proportional to the cross-impedance $Z_{34}$. Dark grey: metal contacts covering the QH structure.