Quantum effects in a superconducting glass model

TL;DR

This paper investigates quantum effects in a disordered Josephson junction array model with long-range interactions, revealing a spin-glass phase destabilized by quantum fluctuations, and maps its phase diagram using advanced theoretical methods.

Contribution

It introduces a comprehensive analysis of quantum fluctuations in a disordered Josephson junction array with long-range interactions, extending spin-glass theory to this quantum superconducting system.

Findings

Identification of a spin-glass like ground state induced by disorder and magnetic field.

Quantum fluctuations destabilize the spin-glass phase at high charging energies.

Phase diagram mapping across temperature and charging energy regimes.

Abstract

We study disordered Josephson junctions arrays with long-range interaction and charging effects. The model consists of two orthogonal sets of positionally disordered $N$ parallel filaments (or wires) Josephson coupled at each crossing and in the presence of a homogeneous and transverse magnetic field. The large charging energy (resulting from small self-capacitance of the ultrathin wires) introduces important quantum fluctuations of the superconducting phase within each filament. Positional disorder and magnetic field frustration induce spin-glass like ground state, characterized by not having long-range order of the phases. The stability of this phase is destroyed for sufficiently large charging energy. We have evaluated the temperature vs charging energy phase diagram by extending the methods developed in the theory of infinite-range spin glasses, in the limit of large magnetic field. The phase diagram in the different temperature regimes is evaluated by using variety of methods, to wit: semiclassical WKB and variational methods, Rayleigh-Schr\"{o}dinger perturbation theory and pseudospin effective Hamiltonians. Possible experimental consequences of these results are briefly discussed.