New model for system of mesoscopic Josephson contacts

TL;DR

This paper introduces a quantum-cosine model with trigonometric phase operators to study quantum fluctuations in 2D arrays of mesoscopic Josephson junctions, revealing differences from macroscopic systems and discussing reentrant superconductivity.

Contribution

It proposes a new model employing trigonometric phase operators suitable for small particle number systems, improving upon previous approaches that used the phase operator and particle number operator as conjugates.

Findings

Significant differences in phase diagrams between macroscopic and mesoscopic arrays for small particle numbers.

Identification of conditions ($n_0<5$, $U<J$) where quantum fluctuations notably affect superconductivity.

Discussion of reentrant superconductivity phenomena in mesoscopic Josephson systems.

Abstract

Quantum fluctuations of the phases of the order parameter in 2D 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 filled with 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 ones 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 particle per granule and $J$ is the Josephson coupling constant). Reentrant superconductivity phenomena are discussed.