Moment of inertia of superconductors

Abstract

We find that the bulk moment of inertia per unit volume of a metal becoming superconducting increases by the amount $m_e/(πr_c)$, with $m_e$ the bare electron mass and $r_c=e^2/m_e c^2$ the classical electron radius. This is because superfluid electrons acquire an intrinsic moment of inertia $m_e (2λ_L)^2$, with $λ_L$ the London penetration depth. As a consequence, we predict that when a rotating long cylinder becomes superconducting its angular velocity does not change, contrary to the prediction of conventional BCS-London theory that it will rotate faster. We explain the dynamics of magnetic field generation when a rotating normal metal becomes superconducting.