"Electro-flux" effect in superconducting hybrid Aharonov-Bohm rings

TL;DR

This paper extends the circuit theory of Andreev conductance to diffusive superconducting hybrid structures with Aharonov-Bohm rings, predicting flux-dependent electrostatic potential and conductance oscillations with the superconducting flux quantum.

Contribution

It introduces a theoretical framework for flux-dependent electrostatic potential and conductance oscillations in superconducting hybrid structures with Aharonov-Bohm rings.

Findings

Electrostatic potential distribution depends on magnetic flux with a period of h/2e.

Conductance oscillates with the same flux quantum period when tunnel barriers are present.

The results generalize the circuit theory to more complex superconducting hybrid systems.

Abstract

We have extended the circuit theory of Andreev conductance [Phys.~Rev.~Lett. {\bf 73}, 1420 (1994)] to diffusive superconducting hybrid structures that contain an Aharonov-Bohm ring. The electrostatic potential distribution in the system is predicted to be flux-dependent with a period of the superconducting flux quantum $\Phi_{0}=h/2e$. When at least one tunnel barrier is present, the conductance of the system oscillates with the same period.