Meissner response of superconductors: Quantum non-locality vs. quasi-local measurements in the conditions of the Aharonov-Bohm effect

Abstract

Theoretical explanation of the Meissner effect involves proportionality between current density and vector potential [1], which has many deep consequences. Amongst them, one can speculate that superconductors in a magnetic field "find an equilibrium state where the sum of kinetic and magnetic energies is minimum" and this state "corresponds to the expulsion of the magnetic field" [2]. This statement still leaves an open question: from which source is superconducting current acquiring its kinetic energy? A naïve answer, perhaps, is from the energy of the magnetic field. However, one can consider situations (Aharonov-Bohm effect), where the classical magnetic field is absent in the space area where the current is being set up. Experiments demonstrate [3] that despite the local absence of magnetic field, current is, nevertheless, building up. From what source is it acquiring its energy then? Locally, only a vector potential is present. How does the vector potential facilitate the formation of the current? Is the current formation a result of truly non-local quantum action, or does the local action of the vector potential have experimental consequences, which are measurable quasi-locally? We discuss possible experiments with a hybrid normal-metal superconductor circuitry, which can clarify this puzzling situation. Experimental answers would be important for further theoretical developments.