Highly-Linear Proximity-Based Bi-SQUID Operating above 4 K

TL;DR

This work addresses the need for highly linear, low-noise cryogenic flux detectors by developing a proximity-based Bi-SQUID amplifier built with three long S-N-S junctions in Nb-Au. The authors fabricate and characterize a single-element Bi-SQUID, showing a sharp, symmetric, and highly linear flux-to-voltage response up to 5 K and estimating a spurious-free dynamic range around 60 dB for a single element. They model the device within an RSJ framework adapted to long diffusive S-N-S junctions, extract parameters indicating notable asymmetry and flux-screening effects, and discuss strategies to improve symmetry and performance. The results suggest that S-N-S Bi-SQUIDs offer a compact, tunable, and robust platform for cryogenic amplification in quantum sensing, magnetometry, and biomedical diagnostics, with clear avenues for further optimization such as gating and localized heating to enhance linearity and noise performance.

Abstract

We demonstrate a highly linear superconducting quantum interference device (SQUID) amplifier based on a double-loop (Bi-SQUID) architecture incorporating three superconductor-normal metal-superconductor (S-N-S) junctions. Fabricated using niobium-gold technology, the device exhibits robust operation at liquid helium temperatures, with a superconducting transition temperature of 8.5 K. The flux-to-voltage transfer function demonstrates sharp, symmetric, and highly linear behavior at temperatures up to 5 K. Bi-SQUIDs featuring our single-element S-N-S design represent an interesting and original approach to this field, as they demonstrate a numerically estimated spurious-free dynamic range (SFDR) linearity exceeding 60 dB, achieved in a single element, simplifying the requirements in terms of arrays containing hundreds of junctions. These results highlight the potential of proximity-based Bi-SQUIDs for compact, low-noise, and highly linear cryogenic amplifiers in quantum sensing, magnetometry, and biomedical diagnostics.

Figures (5)

• Figure 1: Device scheme and SEM image. a) Circuit diagram of the Bi-SQUID. A flux current $I_{flux}$ injected into the external flux line generates magnetic flux $\Phi$ that threads the large loop, but is screened from the small loop by a superconducting layer. Three superconductor-normal metal-superconductor (S-N-S) junctions interrupt the small loop, with one junction shared between both loops. A bias current flows through the device structure while a voltage is measured across it. b) SEM image of the Bi-SQUID viewed from above. The large loop has an internal diameter of 28 $\mu$m, while the small loop has an internal diameter of 8 $\mu$m. c) False-colour SEM image of an S-N-S junction viewed from above. Note that this junction is fabricated using the same process as those used in the Bi-SQUID, but it is not one of the junctions shown in panel b). d) Schematic of the layer structure of the S-N-S junction: a gold (Au) layer with a thickness of 30 nm, length of 800 nm, and width of 300 nm is deposited on SiO$_2$. A 120 nm thick niobium (Nb) layer is deposited on top. This layer is then etched to create a 250 nm gap, which forms the S-N-S junction.
• Figure 2: Current-voltage ($IV$) curves, switching current ($I_s$) and resistance ($R$) as a function of bath temperature ($T_B$). a) Current-voltage ($IV$) curves measured at various bath temperatures ($T_B$). Below 5 K, the curves exhibit hysteretic behaviour with distinct switching and retrapping currents, typical of S-N-S junctions. The pronounced asymmetry between positive and negative bias directions results from flux screening effects, as quantified later in the text. b) Switching current ($I_s$) and retrapping current ($I_r$) as a function of bath temperature ($T_B$). The switching current exhibits a strong temperature dependence, characteristic of long diffusive S-N-S junctions. c) Resistance versus bath temperature of the Bi-SQUID. The data show a single superconducting transition at approximately $T_c=8.5$ K, indicating high junction transparency and proximity effect in the S-N-S junctions, which exhibit the same critical temperature as the niobium leads.
• Figure 3: Switching current ($I_s$) vs magnetic flux applied ($\Phi$). a) Measured switching current ($I_s$) with the superimposed fitted curve of the model obtained from Eq. \ref{['eq:current_balance']}, Eq. \ref{['eq:flux_loop1']}, and Eq. \ref{['eq:flux_loop2']} at $T_B = 4$ K. The magnetic flux is applied by current-biasing the external flux line shown in Figure \ref{['fig:fig1']}(a) and Figure \ref{['fig:fig1']}(b). b) Measured switching current ($I_s$) with superimposed the fitted curve at $T_B = 5$ K.
• Figure 4: Voltage ($V$) as a function of applied magnetic flux $\Phi$ for different bias current applied ($I_{bias}$). a) Four-wire lock-in measurements of voltage ($V$) versus applied magnetic flux ($\Phi$) at $T_B = 4$ K for different bias currents ($I_{bias}$). The device is biased with a periodic ramp signal generated by an arbitrary waveform generator at a frequency of 17 Hz. The ramp modulation sweeps from 0 to the maximum values indicated in the legend, effectively removing the contribution of retrapping current from the voltage measured by the lock-in amplifier. The curves exhibit the sharp shape and highly linear flux-to-voltage transfer function characteristic of a Bi-SQUID. b) Voltage-flux characteristics measured under identical conditions at $T_B = 5$ K. The transfer function maintains its sharp, linear behavior at higher temperatures, demonstrating stable Bi-SQUID performance across the operating temperature range.
• Figure 5: Figures of merit: Maximum spurious-free dynamic range linearity ($L_{SFDR}$) and flux-to-voltage transfer function ($f_{t^M}$) for different temperatures, bias currents, and input flux amplitudes. a) Maximum spurious-free dynamic range linearity ($L_{SFDR}$) as a function of input flux amplitude ($\Phi_{in}$) for different bias currents at $T_B = 4$ K. The linearity is extracted from the voltage-flux response of the Bi-SQUID by numerically applying a sinusoidal flux modulation of amplitude $\Phi_{in}$ to the measured transfer characteristics from Figure \ref{['fig:fig4']}, then analyzing the output signal harmonics using Fast Fourier Transform (FFT). The inset shows the maximum value of the flux-to-voltage transfer function ($f_{t^M}$) as a function of the bias current at 4 K. b) Spurious-free dynamic range estimation under identical conditions at $T_B = 5$ K. The comparable performance at both temperatures demonstrates the robust linearity of the Bi-SQUID flux-to-voltage conversion across the operating range. The inset displays $f_{t^M}$ versus bias current at 5 K.