Momentum of superconducting electrons and the explanation of the Meissner effect

Abstract

Momentum and energy conservation are fundamental tenets of physics, that valid physical theories have to satisfy. In the reversible transformation between superconducting and normal phases in the presence of a magnetic field, the mechanical momentum of the supercurrent has to be transferred to the body as a whole and vice versa, the kinetic energy of the supercurrent stays in the electronic degrees of freedom, and no energy is dissipated nor entropy is generated in the process. We argue on general grounds that to explain these processes it is necessary that the electromagnetic field mediates the transfer of momentum between electrons and the body as a whole, and this requires that when the phase boundary between normal and superconducting phases is displaced, a flow and counterflow of charge occurs in direction perpendicular to the phase boundary. This flow and counterflow does not occur according to the conventional BCS-London theory of superconductivity, therefore we argue that within BCS-London theory the Meissner transition is a `forbidden transition'. Furthermore, to explain the phase transformation in a way that is consistent with the experimental observations requires that (i) the wavefunction $and$ charge distribution of superconducting electrons near the phase boundary extend into the normal phase, and (ii) that the charge carriers in the normal state have hole-like character. The conventional theory of superconductivity does not have these physical elements, the theory of hole superconductivity does.