Phase dipoles: Superconducting analogue of residual resistivity dipoles

Abstract

Current flow in superconductors requires carriers to transmit past a scattering obstacle without developing any applied voltage. Instead, a difference in the macroscopic phase of the superconducting order parameter develops self-consistently as a consequence of the incident carrier flux. The spatial distribution of the order parameter phase has the form of a dipole field. The lack of any voltage difference across the barrier arises from an unusual type of scattering state, where the superfluid flow closes the usual normal reflection channel, allowing only Andreev reflections. We use this scattering state to show that the electromigration force on a scattering defect inside a current carrying superconductor is nearly zero. To complete the picture of the zero voltage, current carrying state in dirty bulk superconductors, we also show that processes which randomize the phase of the individual electronic wavefunctions do not reduce the phase coherence of the superconducting order parameter. The order parameter magnitude is reduced to zero and the superconductivity is lost when the quasiparticle phase-breaking length becomes smaller than the size of a Cooper pair.