Little–Parks effect
The Little–Parks effect was discovered in 1962 by William A. Little and Roland D. Parks in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. It was one of the first experimental indications of the Cooper-pairing principle.
The essence of Little–Parks (LP) effect is slight suppression of the superconductivity by persistent current.
Results schematically shown in the Fig., where we see periodical oscillations of critical temperature (Tc), superimposed on the parabolic background.
The electrical resistance of such cylinders shows a periodic oscillation with the magnetic flux piercing the cylinder, the period being
where h is the Planck constant and e is the electron charge. The explanation provided by Little and Parks is that the resistance oscillation reflects a more fundamental phenomenon, i.e. periodic oscillation of the superconducting Tc.
The LP effect consists in a periodic variation of the Tc with the magnetic flux, which is the product of the magnetic field (coaxial) and the cross sectional area of the cylinder. Tc depends on the kinetic energy (KE) of the superconducting electrons. More precisely, the Tc is such temperature at which the free energies of normal and superconducting electrons are equal, for a given magnetic field. To understand the periodic oscillation of the Tc, which constitutes the LP effect, one needs to understand the periodic variation of the kinetic energy. The KE oscillates because the applied magnetic flux increases the KE while superconducting vortices, periodically entering the cylinder, compensate for the flux effect and reduce the KE. Thus, the periodic oscillation of the kinetic energy and the related periodic oscillation of the critical temperature occur together.
The LP effect is a result of collective quantum behavior of superconducting electrons. It reflects the general fact that it is the fluxoid rather than the flux which is quantized in superconductors.
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