Little-Parks effect

The Little-Parks effect [1] was discovered in 1962 in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field.

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The electrical resistance of such cylinders shows a periodic oscillation with the magnetic flux piercing the cylinder, the period being

h/2e = 2.07e⁻¹⁵ Tm².

The explanation provided by Little and Parks is that the resistance oscillation reflects a more fundamental phenomenon, i.e. periodic oscillation of the superconducting transition critical temperature (Tc). This is the temperature at which the sample becomes superconducting.

The LP effects consists in a periodic variation of the critical temperature with the magnetic flux, which is the product of the magnetic field (coaxial) and the cross section area of the cylinder. Basically, the Tc depends on the kinetic energy of the superconducting electrons. More precisely, the critical temperature 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 (KE). The KE oscillates because the applied magnetic flux increases the kinetic energy while superconducting vortices, periodically entering the cylinder, compensate for the flux effect and reduce the KE [1]. 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 [2].

References

• [1] W. A. Little and R. D. Parks, Physical Review Letters, Vol.9, page 9, (1962).
• [2] M. Tinkham, “Introduction to Superconductivity”, 2nd Ed., McGraw-Hill, NY, 1996.