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

摘要

An array of resistively and capacitively shunted Josephson junctions withnonsinusoidal current-phase relation is considered for modelling the transitionin high-T$_c$ superconductors. The emergence of higher harmonics, besides thesimple sinusoid $I_{c}\sin\phi$, is expected for dominant \emph{d}-wavesymmetry of the Cooper pairs, random distribution of potential drops, dirtygrains, or nonstationary conditions. We show that additional cosine and sineterms act respectively by modulating the global resistance and by changing theJosephson coupling of the mixed superconductive-normal states. First, theapproach is applied to simulate the transition in disordered granularsuperconductors with the weak-links characterized by nonsinusoidalcurrent-phase relation. In granular superconductors, the emergence ofhigher-order harmonics affects the slope of the transition. Then, arrays ofintrinsic Josephson junctions, naturally formed by the CuO$_2$ planes incuprates, are considered. The critical temperature suppression, observed atvalues of hole doping close to $p=1/8$, is investigated. Such suppression,related to the sign change and modulation of the Josephson coupling across thearray, is quantified in terms of the intensities of the first and secondsinusoids of the current-phase relation. Applications are envisaged for thedesign and control of quantum devices based on stacks of intrinsic Josephsonjunctions.