Electromotive interference in a mechanically oscillating superconductor: generalized Josephson relations and self-sustained oscillations of a torsional SQUID
Résumé
We consider the superconducting phase in a moving superconductor and
show that it depends on the displacement flux. Generalized constitutive
relations between the phase of a superconducting interference device
(SQUID) and the position of the oscillating loop are then established.
In particular, we show that the Josephson current and voltage depend
on both the SQUID position and velocity. The two proposed relativistic
corrections to the Josephson relations come from the macroscopic displacement
of a quantum condensate according to the (non-inertial) Galilean covariance
of the Schr\"{o}dinger equation, and the kinematic displacement of
the quasi-classical interfering path. In particular, we propose an
alternative demonstration for the London rotating superconductor effect
(also known as the London momentum) using the covariance properties
of the Schr\"{o}dinger equation. As an illustration, we show how these
electromotive effects can induce self-sustained oscillations of a
torsional SQUID, when the entire loop oscillates due to an applied
dc-current.
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