Quantum Glass Transition in a Periodic Long-Range Josephson Array

TL;DR

This paper demonstrates a quantum glass transition in a periodic long-range Josephson array under magnetic frustration, revealing a transition from a superconducting glass to an insulating state with specific critical scaling behaviors.

Contribution

It introduces the concept of a quantum glass transition in a disorder-free Josephson array and characterizes its critical scaling near the transition point.

Findings

The ground state is a glass with non-zero phase stiffness at large Josephson energies.

The glass state becomes insulating with reduced Josephson energies.

Critical behavior includes a vanishing excitation gap as (J-J_c)^2 and a specific magnetic susceptibility scaling.

Abstract

We show that the ground state of the periodic long range Josephson array frustrated by magnetic field is a glass for a sufficiently large Josephson energies despite the absence of a quenched disorder. Like superconductors, this glass state has non-zero phase stiffness and Meissner response; for smaller Josephson energies the glass "melts" and the ground state loses the phase stiffness and becomes insulating. We find the critical scaling behavior near this quantum phase transition: the excitation gap vanishes as (J-J_c)^2, the frequency-dependent magnetic susceptibility behaves as \chi(\omega) ~ \sqrt{\omega}\ln{\omega}.