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Japanese Journal of Applied Physics

“Effective” Magnetic Flux of NbN Nanobridges in a dc-SQUID

Tsutomu Yamashita, Katsuhiro Hosokawa

Published Mar 1, 1987• 3 citations
Publisher

Abstract

An investigation was carried out to discover whether the “effective” magnetic flux Φeff (=“effective” inductance times dc supercurrent) of a Josephson junction is detectable or not. In the experiment, the internal flux of a dc-SQUID with NbN nanobridges was measured using a SQUID fluxmeter. It was found that the internal flux of a dc-SQUID is strongly affected by the “effective” flux of Josephson junctions.

DOI
10.1143/jjap.26.391

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IEEE Transactions on Applied Superconductivity•Apr 18, 2018•1 citation
An investigation was carried out to discover whether the “effective” magnetic flux Φeff (=“effective” inductance times dc supercurrent) of a Josephson junction is detectable or not. In the experiment, the internal flux of a dc-SQUID with NbN nanobridges was measured using a SQUID fluxmeter. It was found that the internal flux of a dc-SQUID is strongly affected by the “effective” flux of Josephson junctions.
Abstract NbN nanobridge dc SQUIDs were fabricated by the field evaporation method and their noise characteristics were evaluated. The fabricated device has a magnetic flux‐voltage conversion efficiency Φ of about 2.5 mV/Φ0 and hence the device has a higher gain than that of the tunneling‐type device with a resistive shunt. The energy resolution is as small as 40 h. When the fabricated SQUID was installed in an FLL circuit and the dynamic range was measured, it is found that an output is proportional to the input for the input magnetic flux of ±32Φ0 without removing the lock. The magnetic flux resolution of the FLL circuit used is 9 × 10−10 Φ02/Hz in the white noise region (at 3 kHz). In the low‐frequency region less than 100 Hz, the 1/f noise described by 5.8 × 10−8 (1/f)Φ02/Hz was observed. This value of the magnetic flux resolution is large by one order of magnitude than that inherent to the device and the noise of the electronics is predominant.
For the fabrication of nanoscale SQUIDs, for example having loop diameters of order 1 µm or smaller, the conventional trilayer window-type Josephson junctions are too large. Instead, we consider the use of nanobridge junctions with dimensions of order 100 nm. The problem of hysteresis in the junctions' current–voltage characteristic (IVC) is avoided by depositing a gold overlayer, which serves as both a thermal and electrical shunt. Noise measurement of dc SQUIDs which incorporate such Nb nanobridges as the Josephson junctions are reported. Devices having different IVCs were fabricated and characterized. The best device has a flux noise of 5 × 10 −6 Φ 0 Hz −1/2 at 4.2 K, and there is no significant increase in the noise level in a static magnetic field up to 2 mT. Techniques for increasing the voltage modulation depth, and hence improving the flux noise performance, are discussed.
Integrated NbN direct current superconducting quantum interference device (DC-SQUID) magnetometers were developed based on high-quality epitaxial NbN/AlN/NbN Josephson junctions for SQUID applications operating at high temperatures. We report the current–voltage and voltage–flux characteristics and the noise performance of the NbN DC-SQUIDs for temperatures ranging from 4.2 to 9 K. The critical current and voltage swing of the DC-SQUIDs decreased by 15% and 25%, respectively, as the temperature was increased from 4.2 to 9 K. The white flux noise of the DC-SQUID magnetometer at 1 kHz increased from 3.9 μΦ0/Hz1/2 at 4.2 K to 4.8 μΦ0/Hz1/2 at 9 K with 23% increase, corresponding to the magnetic field noise of 6.6 and 8.1 fT/Hz1/2, respectively. The results show that NbN DC-SQUIDs improve the tolerance of the operating temperatures and temperature fluctuations in SQUID applications.
The standard operation of a dc SQUID leads to oscillatory electric fields that emit electromagnetic radiation. We estimate the effect that this radiation could have on the measured sample. A stationary SQUID could be advantageous if the oscillation contribution to back action on the measured sample has to be avoided. We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows across the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime, i.e. the densities of normal current and of supercurrent become functions of position only, independent of time. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The influence of thermal noise was estimated. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.
Nanoscale superconducting quantum interference devices (nano-SQUIDS) where the weak links are made from nanobridges, i.e., nanobridge SQUIDs (NBSs), are one of the most sensitive magnetometers for nanoscale magnetometry. Because of very strong nonlinearity in the nanobridge-electrode joints, the applied magnetic flux (${\mathrm{\ensuremath{\Phi}}}_{a}$)--critical current (Ic{I}_{c}Ic​) characteristics of NBSs differ very significantly from conventional tunnel-junction SQUIDs, especially when the nanobridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated as the conventional tunnel-junction SQUIDs, which are based on the dc Josephson effect. Here, I present a model demonstrating that for long nanobridges and/or large screening parameters the ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$ of a NBS can be explained by merely considering the fluxoid quantization in the NBS loop and the energy of the NBS; it is not necessary to take the Josephson effect into consideration. I also demonstrate that using the model, one can derive useful expressions such as the modulation depth and transfer function. I discuss the role of the kinetic inductance fraction ($\ensuremath{\kappa}$) in determining ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$. I compare the predictions of the present model with the experimental data already published by several groups.
Planar niobium nitride (NbN) dc superconducting quantum interference devices (SQUIDs) magnetometers were developed based on high-quality epitaxial NbN/AlN/NbN Josephson junctions for SQUID applications at higher operating temperatures. To improve the design of NbN dc SQUIDs, we measured the SQUID washer's inductance, which is a key SQUID parameter. A set of NbN dc SQUIDs with washers with different dimensions were implemented. The washer inductances were obtained from the periodic flux variation in the SQUIDs when a control current was injected directly into the SQUID washers; the results agree well with the ones calculated with a numerical simulation in InductEX software. We obtained an empirical expression to estimate the NbN SQUID inductance with washers with different geometric structures. Our results will be useful for designing NbN dc SQUID magnetometers in future.