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arXiv:0806.3187 · Superconductor Science and Technology

On transmission line resonances in highTCdc SQUIDs

U Sinha, A Sinha, E J Tarte

Published Jun 18, 2008• 3 citations
arXivHTMLPDF

Abstract

In this paper, we study transmission line resonances in high T C dc SQUIDs (superconducting quantum interference devices). These resonances are exhibited in the characteristics of SQUIDs which are fabricated on substrates with high dielectric constant, such as strontium titanate. The power balance equation is analytically derived both for symmetric and for asymmetric SQUIDs. Using this, we investigate SQUID current–voltage I ( V ), voltage–flux V (Φ) and voltage modulation Δ V characteristics.

DOI
10.1088/0953-2048/21/8/085021

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In this paper, we study transmission line resonances in high T C dc SQUIDs (superconducting quantum interference devices). These resonances are exhibited in the characteristics of SQUIDs which are fabricated on substrates with high dielectric constant, such as strontium titanate. The power balance equation is analytically derived both for symmetric and for asymmetric SQUIDs. Using this, we investigate SQUID current–voltage I ( V ), voltage–flux V (Φ) and voltage modulation Δ V characteristics.
Effects of large dielectric constant of SrTiO3 substrate on the characteristics of high Tc dc superconducting quantum interference device (SQUID) are studied theoretically. It is shown that parasitic capacitance, which is caused by the substrate and distributes along an inductance of the SQUID, cannot be neglected when we use SrTiO3 substrate. Due to the distributed parasitic capacitance, the inductance can no longer be described as lumped element, but behaves like a transmission line when the length of the inductance becomes long. Taking into account the resonant characteristics of the transmission line, we have modified the conventional equivalent circuit of the SQUID, and presented a circuit model for this case. Using numerical simulation, we have clarified quantitatively how the SQUID characteristics are affected by the resonance due to the parasitic capacitance. The obtained results indicate the importance of taking into account the resonance when we use the SrTiO3 substrate, especially for the case of large junction resistance. Numerical simulation of the model cases shows the possibility that the transfer function can be much increased without degrading the flux noise when the SQUID is properly designed. The present theoretical results explain well the experimental results reported recently.
We have designed, fabricated, and tested a Double Transformer (DT) coupled dc SQUID (Superconducting Quantum Interference Device) with low noise, an input inductance of 1μH and a smooth input-output characteristic. A transmission line model is presented to explain a resonance in the input-output characteristic of early versions of this device. Guided by the results of numerical simulations a new version of this device has been built and tested. Experimental results are presented that show that the resonance can be moved to a higher voltage by reducing the area of the SQUID loop. The voltage-external flux characteristic of some of these new devices agrees to within 10% with computer simulations. The minimum detectable energy per unit bandwidth (MDE) referred to the SQUID loop, is 10h, where h is Planck's constant. Computer simulations indicate an MDE of 6h.
The output voltage of a dc superconducting quantum interference device (SQUID) containing a resistive section Rs oscillates at a frequency νq =Vs/ φ0 (φ0=flux quantum) when a current controlled voltage Vs is maintained across Rs. These oscillations have been observed from ∼10−1 to 1011 Hz, using Rs values ranging from ∼10−10 to ∼10−3 Ω in low inductance (∼10−10 H) point contact SQUID loops. At high frequencies, they manifest themselves in the dc current-voltage characteristics by inducing extra current steps.
The dynamics and noise of a dc SQUID (the Superconducting Quantum Interference Device), with the McCumber parameter /spl beta//sub c/=2/spl pi/R/sup 2/l/sub c/C//spl Phi//sub 0/ close to the unity (where I/sub c/, R, C is the critical current, the shunt resistance and the capacitance of the Josephson junctions comprising the SQUID, respectively, /spl Phi//sub 0/=2.07 10/sup -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 so as to match its /spl lambda//4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance is found to enhance the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, to increase the dynamic resistance R/sub d/ and the gradient of the flux-to-voltage characteristics, /spl delta/V//spl delta//spl Phi/, without hysteresis. A dc SQUID with a loop inductance L=30.5 pH, /spl beta//sub c/=0.72, and a 6 turn input coil demonstrated a non-distorted quasi-sinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of 140 /spl mu/V peak-to-peak. The spectral density of the magnetic flux noise was as low as 3.5/spl times/10/sup -7/ /spl Phi//sub 0//Hz/sup 1/2/ in the double stage configuration, measured at a temperature 4.2 K using direct read out electronics. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz/sup 1/2/ with an input coil inductance of 100 nH.
We have fabricated direct-injection high-Tc superconducting quantum interference devices (SQUIDs) with integrated YBa2Cu3O7−x (YBCO) ground planes in the upper part of structure. The YBCO/PrBa2Cu3O7−x(PBCO)/YBCO edge junctions with 10-nm-thick PBCO barriers showed RSJ-like current-voltage (I–V) characteristics before and after the ground plane formation. We measured the voltage modulations of these SQUIDs with two different hole sizes to evaluate the line inductance. At a temperature of 30 K, the estimated line inductance under the ground plane was about 1.0 pH/□, while the estimated line inductance without the ground plane was 2.8 pH/□.
The LC\mathrm{LC}LC (inductance-capacitance) resonance phenomenon in the dc SQUID (superconducting quantum interference device) creates a current peak in the $I\ensuremath{-}V$ characteristics at a voltage determined by the resonance frequency. These $I\ensuremath{-}V$ characteristics have been analyzed with the resistively shunted Josephson-junction model in the low-damping and small-oscillation regime. The resonance $I\ensuremath{-}V$ characteristics contain sufficient information to determine all circuit parameters for the dc SQUID's. Specifically, we can apply this analysis to symmetric, tunnel-junction dc SQUID's to deduce the pair-quasiparticle interference conductance ($cos\ensuremath{\theta}$ term).