Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder

TL;DR

This study uses large-scale simulations to explore how positional disorder affects the phase transition types and critical behaviors in 2D Josephson junction arrays, revealing a transition from BKT to non-BKT types with increasing disorder.

Contribution

It provides the first numerical evidence that strong positional disorder induces a non-BKT phase transition in 2D Josephson junction arrays, aligning with recent experimental findings.

Findings

Phase transition occurs at nonzero temperature in both weak and strong disorder regimes.

Weak disorder exhibits BKT-type transition; strong disorder shows non-BKT transition.

Critical parameters (T_c, ν, z) match those of the 2D gauge-glass model.

Abstract

We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current voltage characteristics reveals an evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment %by Yun {\it et al.} in cond-mat/0509151 on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of $E_J/k_B$ with the Josephson coupling strength $E_J$), the correlation length critical exponent $\nu=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.