Phase diagram of 2D array of mesoscopic granules

TL;DR

This paper investigates the phase diagram of a 2D array of mesoscopic granules using a lattice boson model, revealing how quantum fluctuations and boson density influence the transition to superconducting order.

Contribution

It provides a combined analytical and numerical analysis of the phase diagram, highlighting the effects of quantum fluctuations and boson density on ordering phenomena in mesoscopic arrays.

Findings

Superconducting boundary shifts to lower temperatures with increasing boson density.

Mesoscopic phenomena persist up to boson density ~10 in weak quantum fluctuation regimes.

Quantum Monte Carlo results agree with mean field and $1/n_0$ expansion theories.

Abstract

A lattice boson model is used to study ordering phenomena in regular 2D array of superconductive mesoscopic granules, Josephson junctions or pores filled with a superfluid helium. Phase diagram of the system, when quantum fluctuations of both the phase and local superfluid density are essential, is analyzed both analytically and by quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density $n_0$ is increased the boundary of ordered superconducting state shifts to {\it lower temperatures} and at $n_0 > 8$ approaches its limiting position corresponding to negligible relative fluctuations of moduli of the order parameter (as in an array of "macroscopic" granules). In the region of weak quantum fluctuations of phases mesoscopic phenomena manifest themselves up to $n_0 \sim 10$. The mean field theory and functional integral $1/n_0$ - expansion results are shown to agree with that of quantum Monte Carlo calculations of the boson Hubbard model and its quasiclassical limit, the quantum XY model.