Phase transitions in a Kagome lattice of Josephson junctions

TL;DR

This paper explores phase transitions in a Josephson junction Kagome lattice under magnetic field, revealing a universal superfluid density jump and a sequence of ground states influenced by frustration.

Contribution

It demonstrates the occurrence of a Kosterlitz-Thouless transition with a universal jump in superfluid density and identifies a sequence of ground states related to flux quanta, advancing understanding of frustrated Josephson systems.

Findings

Phase transition at coupling energy 0.078 observed.

Universal superfluid density jump consistent with Kosterlitz-Thouless theory.

Sequence of ground states with flux quanta per triangle identified.

Abstract

We investigate the nature of the phase transition in Josephson junctions arranged on a Kagome lattice. We find that an applied magnetic field corresponding to 1/2 flux quanta per elementary triangle results in a pi phase shift in the current phase relation for all bonds, resulting in an XY antiferromagnet. This corresponds to the order-from-disorder selected highly-degenerate coplanar state of the more extensively studied Heisenberg Kagome antiferromagnet. Using an histogram Monte-Carlo analysis, we observe a phase transition at 0.078 of the coupling energy. We find that the jump in the superfluid density at the transition temperature, determined from a finite-size scaling analysis of the magnetization fluctuations, retains its universal value within the Kosterlitz-Thouless scenario despite the well-known degeneracy of the low-temperature phase. This universal jump, combined with the dramatically suppressed transition temperature, point to a very strong renormalization of the spin stiffness just below the transition temperature. We also observe a sequence of ground states corresponding to flux quanta per elementary triangle of 1/2, 3/8, 1/4, 1/8, and 0 that, unlike ground states of other lattices, consist of currents of equal magnitude circulating around each elementary triangle in the structure. This sequence of structurally similar ground states will permit a detailed analysis of the dependence of transition temperature on frustration.