^{1,a)}, Marco Gilli

^{2,b)}, Piero Mazzetti

^{2,c)}and Linda Ponta

^{2,d)}

### Abstract

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modeling the transition in high-superconductors. The emergence of higher harmonics, besides the simple sinusoid , is expected for dominant -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 planes in cuprates, are considered. The critical temperature suppression, observed at values of hole doping close to , 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.

The Istituto Superiore per le Telecomunicazioni M. Boella is gratefully acknowledged for financial support.

I. INTRODUCTION

II. NONSINUSOIDAL RCSJ MODEL

A. Resistive transition in granular superconductors

B. Critical temperature anomaly in cuprates

III. CONCLUSIONS

### Key Topics

- Josephson junctions
- 56.0
- Critical currents
- 24.0
- Electrical resistivity
- 22.0
- Superconductors
- 22.0
- Josephson effect
- 17.0

## Figures

(a) Two-dimensional Josephson junction array representing a granular superconductor. Circles represent superconducting grains. Crosses represent weak-links between grains. The bias current is injected to the left electrode and collected from the right electrode. (b) Equivalent circuit of the weak-link between the grains and . The linear resistor , the linear capacitor , the nonlinear inductor and memristor are connected in parallel. The current flows from grain to grain . is the voltage drop across the weak-link.

(a) Two-dimensional Josephson junction array representing a granular superconductor. Circles represent superconducting grains. Crosses represent weak-links between grains. The bias current is injected to the left electrode and collected from the right electrode. (b) Equivalent circuit of the weak-link between the grains and . The linear resistor , the linear capacitor , the nonlinear inductor and memristor are connected in parallel. The current flows from grain to grain . is the voltage drop across the weak-link.

Josephson junction characteristics of a weak-link with current-phase relation (a) ; (b) with and ; (c) with and . The generalized Stewart–McCumber parameter is .

Josephson junction characteristics of a weak-link with current-phase relation (a) ; (b) with and ; (c) with and . The generalized Stewart–McCumber parameter is .

Resistive transition of a two-dimensional network with current-phase relation of the form . The average value of the critical current is 1 mA. The curves correspond to different average values of the critical current , namely , , , and . The normal resistance is equal for all the junctions.

Resistive transition of a two-dimensional network with current-phase relation of the form . The average value of the critical current is 1 mA. The curves correspond to different average values of the critical current , namely , , , and . The normal resistance is equal for all the junctions.

Resistive transition of a two-dimensional network with current-phase relation of the form . The average value of the critical current is 1 mA. The curves correspond to different average values of the critical current , namely, , , , and . The normal resistance is equal for all the junctions. Panels (b) and (c) show the details of the beginning and the end of the transition.

Resistive transition of a two-dimensional network with current-phase relation of the form . The average value of the critical current is 1 mA. The curves correspond to different average values of the critical current , namely, , , , and . The normal resistance is equal for all the junctions. Panels (b) and (c) show the details of the beginning and the end of the transition.

Arrays of intrinsic Josephson junctions are naturally formed in cuprates by the planes separated by layers of insulating atoms. The hole doping of the planes affects transport and thermodynamic properties of cuprates. Several transport anomalies have been observed around that cannot be explained in the framework of a conventional picture of the intrinsic Josephson junctions and have been ascribed to the antiphase ordering across the planes (Refs. 51–57). The modulation of the phase can be taken into account by using the proposed array of resistively and capacitively nonsinusoidal Josephson junctions.

Arrays of intrinsic Josephson junctions are naturally formed in cuprates by the planes separated by layers of insulating atoms. The hole doping of the planes affects transport and thermodynamic properties of cuprates. Several transport anomalies have been observed around that cannot be explained in the framework of a conventional picture of the intrinsic Josephson junctions and have been ascribed to the antiphase ordering across the planes (Refs. 51–57). The modulation of the phase can be taken into account by using the proposed array of resistively and capacitively nonsinusoidal Josephson junctions.

Critical temperature as a function of the hole doping . The ideal parabolic relation is plotted as a reference (solid line). Circles are experimental data obtained on YBCO samples with varying doping level of the planes (Ref. 66). The suppression of in the range of doping between 0.08 and 0.17 can be observed.

Critical temperature as a function of the hole doping . The ideal parabolic relation is plotted as a reference (solid line). Circles are experimental data obtained on YBCO samples with varying doping level of the planes (Ref. 66). The suppression of in the range of doping between 0.08 and 0.17 can be observed.

Critical temperature (a) and currents (b) as a function of the hole doping . The data are obtained by simulating the network of Josephson junctions with current-phase relation given by . The average critical current of the array takes values in the range 1–10 mA. In order to yield the suppression of as a function of the doping level the component is reduced. In the inset of (b) the ratio of the components corresponding to the ideal parabolic behavior and the real curve is plotted.

Critical temperature (a) and currents (b) as a function of the hole doping . The data are obtained by simulating the network of Josephson junctions with current-phase relation given by . The average critical current of the array takes values in the range 1–10 mA. In order to yield the suppression of as a function of the doping level the component is reduced. In the inset of (b) the ratio of the components corresponding to the ideal parabolic behavior and the real curve is plotted.

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