Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

TL;DR

This study investigates the superconductor-insulator transition in Josephson-junction arrays on a honeycomb lattice under magnetic flux, revealing different transition orders and universality classes compared to square lattices, with implications for experimental systems.

Contribution

It provides the first detailed Monte Carlo analysis of the transition on a honeycomb lattice, identifying transition types and critical exponents distinct from other lattice geometries.

Findings

Transition is first order at f=1/3 and continuous at f=1/2.

Critical exponents differ from those on square lattices.

Universal conductivity at the transition is approximately four times higher than at zero flux.

Abstract

We study the superconductor to insulator transition at zero temperature in a Josephson-junction array model on a honeycomb lattice with $f$ flux quantum per plaquette. The path integral representation of the model corresponds to a (2+1)-dimensional classical model, which is used to investigate the critical behavior by extensive Monte Carlo simulations on large system sizes. In contrast to the model on a square lattice, the transition is found to be first order for $f=1/3$ and continuous for $f=1/2$ but in a different universality class. The correlation-length critical exponent is estimated from finite-size scaling of vortex correlations. The estimated universal conductivity at the transition is approximately four times its value for $f=0$. The results are compared with experimental observations on ultrathin superconducting films with a triangular lattice of nanoholes in a transverse magnetic field.