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We consider the superconducting phase in a moving superconductor and showthat it depends on the displacement flux. Generalized constitutive relationsbetween the phase of a superconducting interference device (SQUID) and theposition of the oscillating loop are then established. In particular, we showthat the Josephson current and voltage depend on both the SQUID position andvelocity. The two proposed relativistic corrections to the Josephson relationscome from the macroscopic displacement of a quantum condensate according to the(non-inertial) Galilean covariance of the Schr\"{o}dinger equation, and thekinematic displacement of the quasi-classical interfering path. In particular,we propose an alternative demonstration for the London rotating superconductoreffect (also known as the London momentum) using the covariance properties ofthe Schr\"{o}dinger equation. As an illustration, we show how theseelectromotive effects can induce self-sustained oscillations of a torsionalSQUID, when the entire loop oscillates due to an applied dc-current.

europhysics letters

Electromotive interference in a mechanically oscillating superconductor:  generalized Josephson relations and self-sustained oscillations of a  torsional SQUID