New model for systems of mesoscopic Josephson junctions

Quantum fluctuations of the phases of the order parameter in two-dimensional arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores containing superfluid helium, or Josephson junctions in which the average number of particles n ₀ (effective bosons, He atoms, and so on) is small, and the standard approach employing the phase operator and the particle number operator as conjugate operators is inapplicable. There is a large difference in the phase diagrams between arrays of macroscopic and mesoscopic objects for n ₀<5 and U<J (U is the characteristic interaction energy of the particles per granule and J is the Josephson coupling constant). Re-entrant superconductivity phenomena are discussed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 649–654 (25 November 1997)