Long-range effect of a Zeeman field on the electric current through the helical metal-superconductor interface in an Andreev interferometer

It is shown that the spin-orbit and Zeeman interactions result in phase shifts of Andreev-reflected holes propagating at the surface of a topological insulator, or in Rashba spin-orbit-coupled two-dimensional normal metals, which are in contact with an s-wave superconductor. Due to interference of holes reflected through different paths of the Andreev interferometer the electric current through external contacts varies depending on the strength and direction of the Zeeman field. It also depends on mutual orientations of Zeeman fields in different shoulders of the interferometer. Such a nonlocal effect is a result of the long-range coherency caused by the superconducting proximity effect. This current has been calculated within the semiclassical theory for Green's functions in the diffusive regime, by assuming a strong disorder due to elastic scattering of electrons.