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

Abstract

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 non-local interaction that facilitates a long-distance information transfer in the direction opposite to electron flow. We compute the supercurrent for several interaction models, including that of an external circuit.

Interaction-induced supercurrent in quantum Hall setups

“…This differs from the answer given in 26 by the inclusion of the dynamical phase χ 21 that effectively shifts the superconducting phase difference. The dynamical phase is invariant with respect to time reversal while the superconducting phase is not, so one may wonder why those two match each other.…”

“…We have not considered the electrostatic potential in 26 . The resulting Matsubara Green function G(ω; x, x ) is a 2 × 2 matrix in Nambu space and satisfies…”

“…Let us specify the interaction to the model used in 26 . To realize a non-local interaction that transfers the electric signals upstream, one embeds the QHE edge into an external electric circuit ( Fig.…”

“…Beenakker 18 has proposed an experimental setup for probing annihilation probability between Bogoliubov quasiparticles from two superconducting source with a phase difference between them with the goal to demonstrate their Majorana nature. The Quantum Hall setups may include more than two superconducting electrodes, such multi-terminal superconducting structures are under active theoretical and experimental investigation [19][20][21][22][23][24][25] Recently the authors have addressed the supercurrents in a long chiral edge channel with two superconducting electrodes 26 . While this current vanishes in approximation of non-interacting electrons, we have shown the possibility of an interaction-induced supercurrent.…”

Two-terminal transport along a proximity-induced superconducting quantum Hall edge

“…This experimental breakthrough offers an opportunity to test the predictions of earlier theoretical works such as the tunneling current from a superconducting point contact into a quantum Hall liquid [11] and the critical current [12] along with the upstream information transfer [13] in a superconductor-normal metal-superconductor (SNS) junction, where the normal metal is in the quantum Hall regime. Furthermore, if one can extend the stable proximity effect into the fractional quantum Hall regime, one might be able to create novel excitations with nontrivial braiding statistics [14][15][16][17].…”