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Applied Physics Letters

Hysteresis and intermittency in direct-current superconducting quantum interference device with nanobridges fabricated on a thin membrane

Eran Segev, Oren Suchoi, Oleg Shtempluck, Fei Xue, Eyal Buks

Published Jan 31, 2011• 4 citations
Publisher

Abstract

This study examined the voltage response of nanobridge-based direct-current superconducting quantum interference devices (dc-SQUIDs) fabricated on a Si3N4 membrane. Such a configuration may help in reducing 1/f noise, which possibly originates from substrate fluctuating defects. Results showed that the poor thermal coupling between the dc-SQUID and the substrate leads to a strong hysteretic response of the superconducting quantum interference device (SQUID) even though it is biased by an alternating current. In addition, when the dc-SQUID is biased near a threshold of spontaneous oscillations, the measured voltage has an intermittent pattern, which depends on the applied magnetic flux threading the loop of the SQUID.

DOI
10.1063/1.3549767

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This study examined the voltage response of nanobridge-based direct-current superconducting quantum interference devices (dc-SQUIDs) fabricated on a Si3N4 membrane. Such a configuration may help in reducing 1/f noise, which possibly originates from substrate fluctuating defects. Results showed that the poor thermal coupling between the dc-SQUID and the substrate leads to a strong hysteretic response of the superconducting quantum interference device (SQUID) even though it is biased by an alternating current. In addition, when the dc-SQUID is biased near a threshold of spontaneous oscillations, the measured voltage has an intermittent pattern, which depends on the applied magnetic flux threading the loop of the SQUID.
We study the metastable response of a highly hysteretic dc superconducting quantum interference device (SQUID) made of a niobium loop interrupted by two nanobridges. We excite the SQUID with an alternating current and with direct magnetic flux, and find different stability zones forming diamond-like structures in the measured voltage across the SQUID. When such a SQUID is embedded in a transmission line resonator, similar diamond structures are observed in the reflection pattern of the resonator. We calculate the dc-SQUID stability diagram in the plane of the exciting control parameters, both analytically and numerically. In addition, we obtain numerical simulations of the SQUID equations of motion, taking into account temperature variations and nonsinusoidal current-phase relation of the nanobridges. Good agreement is found between experimental and theoretical results.
We have fabricated two types of NbN nanobridge dc Superconducting QUantum Interference Devices (SQUIDs). From the analyses of the response to magnetic field, it is found that the current-phase relationship for the planar-type nanobridge and the nanobridge fabricated by field evaporation is close to sinusoidal. For V\gtrsim720 µV, The spectral densities of the voltage noise show linear dependence on the voltage for the SQUIDs with nanobridges whose length is about the superconducting coherence length of NbN. The SQUIDs with nanobridges with lengths of several times the NbN coherence length exhibit parabolic voltage dependence.
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.
We report on the low-frequency noise performance of niobium dc superconducting quantum interference devices (SQUIDs), which contain nanobridges fabricated by focused ion beam lithography as the active Josephson elements. The devices have feature sizes down to 70 nm. We have measured devices of different loop sizes in two readout configurations: nano-scale loop sizes in small signal mode using a series SQUID array as a low-temperature pre-amplifier, and larger micron-scale loop sizes in a conventional flux-locked loop. We investigate the different contributions to the low frequency noise and report on electrical measurements made in applied magnetic fields of up to 0.5 T (in-plane) and 0.1 T (perpendicular to the plane) at operating temperatures around 7 K. We compare the measurements with the existing theories of noise in a dc SQUID.
In the recent years, nanoscale superconducting quantum interference devices (nano-SQUIDs) played a fundamental role in the study of small spin systems. Nano-SQUIDs typically employ nano-Dayem bridges having dimensions (length LLL and/or width WWW) greater than coherence length $\ensuremath{\xi}$ of the superconducting film. They exhibit characteristics different from those of standard SQUIDs because the current-phase relationship (CPR) is nonsinusoidal, rendering most of the theoretical predictions based on the standard SQUID theory usually unreliable. Here, we present a noise theory of dc nano-SQUIDs based on Dayem nanobridges. We have computed the main characteristics of this quantum device including current-voltage and voltage-magnetic flux characteristics, magnetic flux-to-voltage transfer factor, and spectral densities of voltage and magnetic flux noise for LLL/$\ensuremath{\xi}$ ratios ranging from 1 (sinusoidal limit) to 3.5 (hysteretic limit). The CPRs have been computed by using the theory of Josephson weak links based on the Ginzburg--Landau equation. The results show a dependence of the magnetic flux noise spectral density on (LLL/$\ensuremath{\xi}$)4/3{}^{4/3}4/3 involving a degradation of about a factor of five between the two extreme cases and are consistent with experimentally measured magnetic flux noises reported in the literature. These results provide useful information for both device physics and their applications.
The dynamics and noise of a dc superconducting quantum interference device (SQUID) with the McCumber parameter βc=2πR2IcC/Φ0 close to the unity (where Ic, R, C are the critical current, the shunt resistance, and the capacitance of the Josephson junctions comprising the SQUID, respectively, and Φ0=2.07×10−15 Wb is the magnetic flux quantum) integrated with a planar spiral input coil have been experimentally studied. The length of the spiral input coil was chosen to match its λ/4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance enhances the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, increases the dynamic resistance Rd and the gradient of the flux-to-voltage characteristics ∂V/∂Φ without hysteresis. This relaxes the tolerance for the βc parameter, simplifies the technological process, and improves the yield of devices. A dc SQUID with loop inductance L=31.4 pH, βc=0.72, and a six turn input coil has demonstrated a nondistorted quasisinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of approximately 140 μV peak-to-peak. A spectral density of the intrinsic magnetic flux noise as low as 3.5×10−7 Φ0/Hz1/2 has been measured in the double stage configuration at a temperature of 4.2 K using direct read-out electronics. This corresponds to the intrinsic energy resolution of ε=12.5h. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz1/2 with an input coil inductance of 58 nH. The coupled energy resolution is εc=45h in the white noise region.