Violation of the London law and Onsager–Feynman quantization in multicomponent superconductors

Abstract

Two quite fundamental principles governing the response to rotation of single-component superfluids and superconductors, the London law [1] relating the angular velocity to a subsequently established magnetic field, and the OnsagerFeynman quantization of superfluid velocity [2,3] are shown to be violated in a two-component superconductor. The manifestation of the two principles normally involves the fundamental constants alone, but this no longer holds as is demonstrated explicitly for the projected liquid metallic states of hydrogen and deuterium at high pressures. The rotational responses of liquid metallic hydrogen or deuterium identify them as a new class of dissipationless states; they also directly point to a particular experimental route for verification of their existence.Non-classical response to rotation is a hallmark of quantum ordered states such as superconductors and superfluids. The rotational responses of all presently known single-component "super" states of matter (superconductors, superfluids and supersolids) are largely described by two fundamental principles and fall into two categories according to whether the systems are composed of neutral or charged particles. For superfluid systems composed of electrically neutral particles (liquids, vapors, or even solids [4]) and for slow rotations, a fraction of the system, the superfluid fraction, remains irrotational. However in response to rotation exceeding a certain critical rotation frequency, the superfluid fraction comes into rotation by means of vortex formation. Onsager and Feynman [2,3] pointed out that the superfluid velocity (v) in these vortices in single-component systems is quantized and the circulation quantum K depends only on particle's mass m and Planck's constant h: K = (1/2π) v · dl =h/m. Here we mention that for superfluids with e.g. p-wave symmetry of the order parameter which are also invariant under simultaneous phase and spin transformations this quantization is modified [5]. We also mention that a special situation occur in a multicomponent superfluid with a dissipationless drag (Andreev-Bashkin effect) where a superfluid velocity of one condensate can carry superfluid density of another [6,7]. Below however we will consider the mixture of charged condensates only with the simplest symmetry of the order parameter coupled by a gauge field.For systems composed of charged particles and which are also superconducting (electronic Cooper pairs in metals, or protonic Cooper pairs in neutron stars) vortices are not induced by rotation; however, the rotational response of these systems is no less interesting. London showed that a uniformly rotating single component superconductor generates a persistent current in a thin layer near its surface, and this in turn produces a detectable magnetic field, the London field [1]. London related this field to the rotation frequency, Ω, according to B = −(2mc/e)Ω, where m is the electron's mass, e denotes it electric charge and c is the speed of light. This law is experimentally confirmed (see ...

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