# Controlling I-V Hysteresis in Al/Pt Bilayer Symmetric SQUIDs at Millikelvin Temperatures

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*Symmetry*)

## Abstract

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## 1. Introduction

## 2. Results and Discussion

## 3. Methods

#### 3.1. E-Beam Lithography and Deposition

#### 3.2. Measurement Details

#### 3.3. Magnetoresistance Oscillation Fitting

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Josephson transport through planar-thin Al/Pt and Al SQUID operations at various temperatures. (

**a**) Scanning electron microscope picture of the device. The voltage across the SQUID is measured at constant ${I}_{bias}$. (

**b**) An image of constriction of 50 × 50 nm. (

**c**) Two types of films form the SQUID, Al and Al/Pt. (

**d**) The non-hysteresis V(I) characteristics of the Al/Pt S1 SQUID taken at $T=$ 0.02–0.8 K. Al/Pt devices have non-hysteresis behavior at all temperature ranges. (

**e**) The hysteresis behaviors of the Al S2 SQUIDs at different temperatures, $T=$ 0.02–1.4 K. (

**f**) The dependencies of the critical and re-trapping currents as functions of T. Al SQUID hysteresis occurs at $T<{T}_{H}=1.25$ K.

**Figure 2.**Comparison of the measured Al/Pt and Al magnetoresistance oscillations. (

**a**,

**b**) Resistance of Al and Al/Pt samples vs. the applied magnetic field and bias current. (

**c**,

**d**) The amplitude of the oscillations, $\mathsf{\Delta}$R vs. bias current defined at low fields.

**Figure 3.**Magnetoresistance oscillations in Al/Pt SQUID with bias current. (

**a**) Al/Pt sample oscillations are described by the RSJ SQUID model. Blue curve: measured magnetoresistance; red curve: theoretical magnetoresistance. Oscillation period: 4.77 G. (

**b**) Theoretical calculations for voltage modulations of SQUID as functions of the magnetic flux for different values of the bias current. The curves correspond from the bottom to the top to the applied control currents of 0.63, 0.75, 0.92, 1.06, 1.25, and 1.37 $\mathsf{\mu}$A, respectively.

Sample | ${\mathit{I}}_{\mathit{c}},\mathsf{\mu}\mathbf{A}$ | ${\mathit{R}}_{\mathit{n}}^{\mathit{exp}},\mathsf{\Omega}$ | ${\mathit{W}}^{\mathit{constriction}},\mathrm{nm}$ | d, nm | L, nm | $\mathit{\delta}\mathit{H},\mathbf{G}$ | ${\mathit{A}}_{\mathit{eff}},\mathsf{\mu}{\mathbf{m}}^{2}$ | ${\mathit{T}}_{\mathit{c}},\mathbf{K}$ | ${\mathit{\rho}}_{\mathit{n}},\mathsf{\Omega}\xb7{nm}$ |
---|---|---|---|---|---|---|---|---|---|

Al/Pt | 2.93 | 23 | 55 ± 2 | 30 ± 1 | 50 ± 10 | 5.3 | 3.8 | 0.8 | 40.93 |

Al | 28.4 | 24 | 52 ± 2 | 25 ± 3 | 50 ± 10 | 4.79 | 4.3 | 1.41 | 35.59 |

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**MDPI and ACS Style**

Yakovlev, D.S.; Nazhestkin, I.A.; Ismailov, N.G.; Egorov, S.V.; Antonov, V.N.; Gurtovoi, V.L. Controlling I-V Hysteresis in Al/Pt Bilayer Symmetric SQUIDs at Millikelvin Temperatures. *Symmetry* **2023**, *15*, 550.
https://doi.org/10.3390/sym15020550

**AMA Style**

Yakovlev DS, Nazhestkin IA, Ismailov NG, Egorov SV, Antonov VN, Gurtovoi VL. Controlling I-V Hysteresis in Al/Pt Bilayer Symmetric SQUIDs at Millikelvin Temperatures. *Symmetry*. 2023; 15(2):550.
https://doi.org/10.3390/sym15020550

**Chicago/Turabian Style**

Yakovlev, Dmitry S., Ivan A. Nazhestkin, Nidzhat G. Ismailov, Sergei V. Egorov, Vladimir N. Antonov, and Vladimir L. Gurtovoi. 2023. "Controlling I-V Hysteresis in Al/Pt Bilayer Symmetric SQUIDs at Millikelvin Temperatures" *Symmetry* 15, no. 2: 550.
https://doi.org/10.3390/sym15020550