Rotational response of superconductors: magneto-rotational isomorphism and rotation-induced vortex lattice

Abstract

The analysis of nonclassical rotational response of superfluids and superconductors was performed by Onsager (in 1949) \cite{Onsager} and London (in 1950) \cite{London} and crucially advanced by Feynman (in 1955) \cite{Feynman}. It was established that, in thermodynamic limit, neutral superfluids rotate by forming---without any threshold---a vortex lattice. In contrast, the rotation of superconductors at angular frequency $\mathbf{\Omega }$---supported by uniform magnetic field ${\mathbf{B}}_L\propto \mathbf{\Omega }$ due to surface currents---is of the rigid-body type (London Law). Here we show that, neglecting the centrifugal effects, the behavior of a rotating superconductor is identical to that of a superconductor placed in a uniform fictitious external magnetic filed $\tilde{\mathbf{H}}=-{\mathbf{B}}_L$. In particular, the isomorphism immediately implies the existence of two critical rotational frequencies in type-2 superconductors.

Comments: replaced with published version