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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Magnetic properties of one-dimensional parallel arrays of Josephson junctions

John H. Miller, Gemunu H. Gunaratne, Zhongji Zou, Matthew F. Davis, H. R. Rampersad, Nong-Qiang Fan, John C. Wolfe

Published Jul 2, 1994• 3 citations

Abstract

A superconducting quantum interference grating (SQUIG), consisting of many Josephson junctions in parallel, exhibits quantum interference analogous to the optical interference pattern produced by a diffraction grating, just as the dc SQUID is the magnetic analog of the double slit in optics. The field- dependent critical current of a SQUIG with sufficiently low inductance exhibits a series of sharp peaks, similar to the position-dependent intensity of a multiple-slit interference pattern. Such a device has the potential for improved sensitivity as a magnetic sensor because of its enhanced flux-to-voltage transfer coefficient. The behavior is quite different, however, when the inductance is large. In this limit, the field-dependent critical current becomes extremely hysteretic and exhibits self- organized phase coherence, in which a peak in the critical current (indicating coherence of the junction phases) is observed after each reversal of the field sweep. We have observed this phenomenon in large inductance arrays with up to ten YBa2Cu3O7 (YBCO) bi-crystal grain boundary junctions in parallel. We have modeled the behavior using a Frenkel-Kontorova model generalized to include global interactions due to mutual inductance. According to our model calculations, self-organized phase coherence occurs when the system relaxes from its critical state, causing the phases to simultaneously relax to minima in the periodic potential representing the Josephson coupling energy, and thus to become coherent modulo 2(pi) .

DOI: 10.1117/12.180987

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A superconducting quantum interference grating (SQUIG), consisting of many Josephson junctions in parallel, exhibits quantum interference analogous to the optical interference pattern produced by a diffraction grating, just as the dc SQUID is the magnetic analog of the double slit in optics. The field- dependent critical current of a SQUIG with sufficiently low inductance exhibits a series of sharp peaks, similar to the position-dependent intensity of a multiple-slit interference pattern. Such a device has the potential for improved sensitivity as a magnetic sensor because of its enhanced flux-to-voltage transfer coefficient. The behavior is quite different, however, when the inductance is large. In this limit, the field-dependent critical current becomes extremely hysteretic and exhibits self- organized phase coherence, in which a peak in the critical current (indicating coherence of the junction phases) is observed after each reversal of the field sweep. We have observed this phenomenon in large inductance arrays with up to ten YBa2Cu3O7 (YBCO) bi-crystal grain boundary junctions in parallel. We have modeled the behavior using a Frenkel-Kontorova model generalized to include global interactions due to mutual inductance. According to our model calculations, self-organized phase coherence occurs when the system relaxes from its critical state, causing the phases to simultaneously relax to minima in the periodic potential representing the Josephson coupling energy, and thus to become coherent modulo 2(pi) .

We have calculated the total critical current as a function of applied magnetic flux for a superconducting interferometer consisting of many Josephson junctions in parallel. An enhancement and narrowing of the periodic principal maxima in the critical current versus flux characteristic is predicted as the number of junctions in parallel increases, even when the effects of finite self- and mutual inductances and nonuniformity of the junction critical currents are included in the calculations. The possible application of the superconducting quantum interference grating, or SQUIG, for the detection of magnetic flux is discussed.

A theoretical study is presented for a number N of Josephson junctions connected as a one-dimensional (1D) parallel array in such a manner that there are $N\ensuremath{-}1$ individual superconducting loops with arbitrary shape formed. In the resistive array mode, for bias currents

I>{I}_{c},

all Josephson junctions in the array oscillate at the same magnetic field dependent frequency ${\ensuremath{\nu}}_{B}$ which is, in general, not a ${\ensuremath{\Phi}}_{0}\ensuremath{-}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{c}$ function of the strength of magnetic field

\mathbf{B}.

Within the range of validity of the resistively and capacitively shunted junction (RCSJ) model the periodicity of ${\ensuremath{\nu}}_{B}$ is controlled by the array geometry alone and does not depend on the distribution of the array junction parameters. In the overdamped junction regime, ${\ensuremath{\nu}}_{B}$ is for certain types of unconventional grating structures a unique function around a sharp global minimum at

\mathbf{B}=0.

This filter property does not apply for regular gratings and superconducting quantum interference devices (SQUID's). Computer simulations of the full nonlinear array dynamics reveal that the qualitative macroscopic quantum interference properties of unconventional arrays are governed, irrespective of the strength of inductive couplings, by a complex structure factor

{S}_{N}(\mathbf{B})

which can be determined analytically. Also, the performance of magnetometers based on 1D arrays with unconventional grating structure can be significantly better than the performance of conventional SQUID's. In particular, 1D arrays with unconventional grating structure should provide a technically rather unsophisticated precision measurement of absolute strength and orientation of external magnetic fields.

This study shows that we can obtain an enhanced mutual coupling by using a superconducting quantum interference device (SQUID) containing a π-phase shift Josephson junction (π-junction). The π-junction can increase the current flowing in the loop inductance of the SQUID, thereby enhancing the magnetic flux generated in the inductance. Therefore, the effective self-inductance of the SQUID can increase, resulting in an increase in the mutual coupling. We use a 0-π SQUID formed by a conventional Josephson junction (0-junction) and a π-junction. Our numerical analysis for a simplified structure revealed that the ratio of effective to original self-inductance increased to 50. To confirm this, we measured the modulation patterns of critical current in dc-SQUIDs in which part of the loop inductance was replaced with a series of 0-π SQUIDs. The observed modulation pattern revealed that the effective self-inductance became more than 10-fold larger than the original self-inductance under the conditions that the applied current is a few μA while the critical current of the 0-junction in 0-π SQUIDs is 35 μA.

Arrays of dc-superconducting quantum interference devices (dc-SQUIDs) were investigated, in which each dc-SQUID element has a multiturn input coil. The dependence of flux noise on the number of turns of the input coil was studied for current amplifiers. SQUID arrays were fabricated by a Nb/AlO x /Nb Josephson tunnel junction fabrication process. Results show that the flux noise of the SQUID array amplifier does not depend on the turn number of the input coil. A SQUID array amplifier consisting of 128 dc-SQUID elements was fabricated, in which each element had a 7-turn input coil and a mutual inductance between the input coil and the SQUID loop of 460 pH. This amplifier showed an ultrahigh current resolution of 1 pA/Hz0.5 and a maximum input current of 11 µA for signals of 50 kHz, which is sufficient bandwidth for X-ray detection applications. These values correspond to a large dynamic range of 87 dB. The flux-voltage characteristics of this SQUID array, however, showed asymmetric behavior, which originated from electronic resonance in stray capacitance and the mutual inductance between the SQUID loop and the multiturn input coil.

The superconducting quantum interference filter (SQIF) is a new type of superconducting device which has been recently proposed for highly sensitive magnetometers for absolute magnetic field measurements. It benefits of very high voltage-to-field response, which is, in contrast conventional dc SQUIDs, not periodical. The SQIF can also be used as a radiofrequency amplifier in a similar way as the dc SQUID that can operate in a gigahertz frequency range. We designed a series type of SQIF amplifier that is compatible to conventional YBa2Cu3O7(YBCO) technology on bicrystal substrates. We present analytical, numerical and scale modeling as well as first electrical measurements results at frequencies up to 10 GHz. The SQIF array consists of 50 loops with randomly distributed areas from 0.5 to 1.5 times of . We also compared it to the regular array of conventional SQUIDs with the same loop areas. We have additional dc contacts to each 5-th SQUIDs and the SQIFs for control and comparison. Devices are fabricated using Josephson junctions with 3 mum width formed in YBCO over 24/24 and 12/12 degrees grain boundaries in yttrium-stabilized zirconia (YSZ) bicrystal substrates.