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Abstract: The magnetic flux periodicity in superconducting loops is reviewed. Whereasquantization of the magnetic flux with hc-2e prevails in sufficiently thickloops with current free interior, the supercurrent in narrow loops is eitherhc-2e or hc-e periodic with the external magnetic flux. The periodicity dependson the properties of the condensate state, in particular on the Doppler shiftof the energy spectrum. For an s-wave superconductor in a loop with diameterlarger than the coherence length, the Doppler shift is small with respect tothe energy gap, and the hc-2e periodic behavior of its flux dependentthermodynamic properties is maintained. However, for smaller s-wave loops and,more prominently, narrow d-wave loops of any diameter R, the Doppler shift hasa strong effect on the supercurrent carrying state; as a consequence, thefundamental flux periodicity is in fact hc-e. It is shown analytically andnumerically that the hc-e periodic component in the supercurrent decays onlyalgebraically as 1-R for large d-wave loops. For nodal superconductors thediscrete nature of the eigenergies close to the Fermi energy has to berespected in the evaluation of the Doppler shift. Furthermore, we investigate,whether the Doppler shift modifies the supercurrent through Josephson junctionswith d-wave superconductors. For transparent junctions, the Josephson currentbehaves similar to the persistent supercurrent in a loop. These distinctphysical phenomena can be compared, if the magnetic flux in units of hc-e isidentified with the phase variation of the order parameter divided by 4 pi.

Autor: Florian Loder, Arno P. Kampf, Thilo Kopp

Fuente: https://arxiv.org/

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