Quantum Phases of a Strongly Disordered Two-Legged Josephson Ladder

TL;DR

This paper investigates the quantum phases of a disordered two-legged Josephson ladder, revealing three distinct phases including a Bose glass and a spin glass, using a strong randomness renormalization group approach.

Contribution

It introduces a model with spatially disordered parameters in a two-legged Josephson ladder that preserves a $ ext{Z}_2$ symmetry and maps out its phase diagram using strong randomness RG techniques.

Findings

Identifies three disorder-dominated phases: superconductor, insulator, and an intermediate Bose glass.

Maps the insulating phase to a spin glass XY chain.

Discovers an intermediate Bose glass phase between superconductor and insulator.

Abstract

Disordered superconductors in low dimensions provide an exemplary manifestation for the role of quantum fluctuations in a many-body system. Specifically in Josephson arrays with comparable Josephson and charging energies ($E_J\sim E_C$), disorder tends to change the nature of the paradigmatic Superconductor-Insulator Transition (SIT) and potentially leads to formation of multiple distinct phases. We address this problem in a model of a two-legged Josephson ladder subjected to a wide spatial distribution of its parameters along the legs. In contrast, we assume the system to have a perfect $\mathbb{Z}_2$ symmetry to interchange between the legs, and investigate the effects of spatial randomness which preserves this symmetry in the strong-disorder limit. To this end, we apply a strong randomness real-space renormalization group technique and explore the resulting phase diagram. We identify three disorder-dominated phases, including an intermediate phase between a disordered superconductor and a disordered insulator. The latter insulating phase can be mapped to a XY spin-chain in a spin glass phase, while the intermediate phase turns out to be a Bose glass.