Flux effect in superconducting hybrid Aharonov-Bohm rings

We have extended the circuit theory of Andreev conductance [Phys. Rev. Lett. {bold 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}{sub 0}={ital h}/2{ital e}. When at least one tunnel barrier is present, the conductance of the system oscillates with the same period. {copyright} {ital 1996 The American Physical Society.}