Non-local transport measurements in hybrid quantum Hall - superconducting devices

There has been a growing interest in hybrid quantum Hall (QH) superconductor devices, driven by the prospect to realize exotic ground states and excitations with non-abelian exchange statistics. While the existing experiments clearly demonstrate Andreev coupling between the edge states and the superconductors, the question remains whether the quantum coherence could propagate between several superconducting contacts via chiral channels. To answer this question, we have first extended the Landauer-B\"uttiker (LB) formalism to samples with one superconducting contact and found a remarkable agreement within a series of measurements related to each other via LB-type formulae. We have then switched to the case of multiple superconducting contacts, and found that we can describe the measurements self-consistently if we neglect the superconducting phase coherence between multiple contacts. We interpret this result as a negative answer to the question posed above: the phase correlations between multiple superconducting contacts are not established via micron-long quantum Hall edge states. Looking forward, our approach may find applications in the broader field of topological superconductivity and proximal structures. Possible violations of the self-consistency tests presented here may be used as an indication that superconducting phase coherence is induced in the quantum Hall edges.