Array of Josephson junctions with a non-sinusoidal current-phase relation as a model of the resistive transition of unconventional superconductors

TL;DR

This paper models the resistive transition in unconventional high-Tc superconductors using arrays of Josephson junctions with non-sinusoidal current-phase relations, highlighting the effects of higher harmonics on superconducting properties.

Contribution

It introduces a novel modeling approach incorporating higher harmonics in Josephson junction arrays to simulate transition behaviors in disordered and cuprate superconductors.

Findings

Higher harmonics modulate the global resistance during transition.

Emergence of higher-order harmonics affects the slope of the superconducting transition.

Critical temperature suppression near doping level p=1/8 is explained by Josephson coupling modulation.

Abstract

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modelling the transition in high-T$_c$ superconductors. The emergence of higher harmonics, besides the simple sinusoid $I_{c}\sin\phi$, is expected for dominant \emph{d}-wave symmetry of the Cooper pairs, random distribution of potential drops, dirty grains, or nonstationary conditions. We show that additional cosine and sine terms act respectively by modulating the global resistance and by changing the Josephson coupling of the mixed superconductive-normal states. First, the approach is applied to simulate the transition in disordered granular superconductors with the weak-links characterized by nonsinusoidal current-phase relation. In granular superconductors, the emergence of higher-order harmonics affects the slope of the transition. Then, arrays of intrinsic Josephson junctions, naturally formed by the CuO$_2$ planes in cuprates, are considered. The critical temperature suppression, observed at values of hole doping close to $p=1/8$, is investigated. Such suppression, related to the sign change and modulation of the Josephson coupling across the array, is quantified in terms of the intensities of the first and second sinusoids of the current-phase relation. Applications are envisaged for the design and control of quantum devices based on stacks of intrinsic Josephson junctions.