S19 Josephson Junction

Magnetic Field Dependence of the Critical Current in Nb-Si-Nb Josephson Junction

Yuka Nakato and Yuhao Yang

University of Minnesota, Methods of Experimental Physics II, Spring 2019

ABSTRACT

The Josephson effect was measured using a Nb-Si-Nb junction cooled to 4.2 K using liquid helium. Voltage data were taken with varied applied current to obtain the I-V characteristics of the junction. The DC magnetic field dependence of the critical current was plotted, and compared to the expected Fraunhofer response. From the minima of the dependence plot, the flux quantum was determined to be

. Compared to the accepted value of [1], this result is off by 5 standard deviations.

INTRODUCTION

In 1962, Brian Josephson predicted an interesting phenomenon using two superconductors separated by a very thin layer of insulating material, a system now called the Josephson junction [2]. His theory showed pairs of electrons, called Cooper pairs, could tunnel through the insulator, up to a maximum applied critical current. This phenomenon is called the DC Josephson effect [1].

Josephson junctions have many practical applications. For instance, they are the building blocks of SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. Josephson junctions can also be used as photon detectors or as electronic mixers, and have promising future applications in areas such as quantum computing. Thus, it is important to study the properties of these junctions; in particular, it is interesting to see how the critical current is affected by factors such as external magnetic field.

In this experiment, the DC Josephson effect was measured using a Nb-Si-Nb junction. The dependence of thee critical current on magnetic field was measured, and compared to existing models.

THEORY

. Thus the current is constant and is given by . The maximum possible value of this current is the critical current

, as it should be. The theoretical I-V plot is shown in Fig. 1.

Fig. 1: Theoretical I-V plot for the DC Josephson effect. There is a supercurrent through the junction up to the maximum applied critical current.

Suppose we apply a magnetic field parallel to the junction, as shown below.

Fig. 2: Josephson junction with an external magnetic field. The field is in the y direction, where the axes are defined on the right. The shaded regions show where the field penetrates into the superconducting electrodes.

and correspond to the London depths in the two superconductors. L, t, and d are the Josephson junction length, insulator thickness, and the magnetic penetration, respectively.

The field induces a difference in throughout the length (x position) of the junction, and thus the current density also becomes dependent on the x position and field strength. Using Fourier analysis, it can be shown that the critical current varies as a function of magnetic flux

:

where is a constant called the flux quantum. The plot of this relationship is shown below. This is called a Fraunhofer pattern, with minima at nonzero integer multiples of the flux quantum.

Fig. 3: The plot of the magnetic field dependence of the critical current.

METHODS

The Nb-Si-Nb junctions for this experiment were chosen from chips manufactured by Univac using the selective niobium anodization process (SNAP) .

Fig. 4: Schematic of a chip manufactured by Univac. Niobium strips (shown in grey) are inlaid diagonally across the chip with another niobium strip inlaid perpendicularly. The purple and green parts are made of insulating material. Squares of silicon of different sizes are layered in between the niobium strips at the intersections, forming the Nb-Si-Nb junctions. The voltage and current four-terminal measurements are made as shown on the fourth junction from the bottom.

A schematic of the experimental setup in Fig. 5 was used to determine the I-V characteristics of the junction. Due to the low resistance of the junction system, we used the four-terminal measurement method. The function generator was used to send a 300 Hz triangle wave to the current source to be converted into the current passing through the junction. The voltage drop across the junction was detected using the differential mode of the pre-amplifier. The initial waveform and the measured differential voltage were sent to the oscilloscope in XY mode to display the I-V characteristics.

Fig. 5: Experimental setup for measuring I-V characteristics of the Josephson junction. The amplifier gain was set to 100.

We used a cryostat-dewar system to cool the junction down to superconducting temperatures. The chip was affixed to the cryostat with a Nb-Ti solenoid wrapped around it and electrical connections extending to the top, as shown on the left in Fig. 6. The cryostat was then fitted into the dewar shown on the right in Fig. 6. Before adding any liquid helium, the system was pre-cooled overnight using liquid nitrogen. This was done in order to prevent the liquid helium from instantly vaporizing due to the temperature difference. Once the internal temperature was down to about 77 K, the liquid helium was added to the inner well to cool the system down to 4.2 K.

Fig. 6: Diagram of the cryostat (left) and Cryofab dewar (right).

Magnetic fields ranging from about -10 G to 10 G were generated by applying DC currents through the solenoid. For each increment of DC solenoid current, the critical current of the junction was determined from the I-V plot. The data were then analyzed using MATLAB and compared to existing models.

RESULTS/ANALYSIS

We successfully observed magnetic field dependent critical currents in our second and third experimental runs (performed using junctions on different chips). Shown in Fig. 7 are the I-V characteristics at zero magnetic field for these runs. The critical currents can be taken from the vertical axis to be 0.016 mA for the second run (left), and 0.11 mA for the third run (right).

Fig. 7: I-V plots for the second run (left) and third run (right) with no applied magnetic field. The voltage controlled current source was set to 1 mA/V and the gain on the amplifier was set to 100.

Especially apparent in the I-V for the third run is a hysteresis that the theoretical I-V in Fig. 1 does not show. In the third run I-V, the forward current sweep on the oscilloscope shows the jump to the resistive state at the critical current 0.11 mA, as expected. However, on the return sweep, the superconducting state reappears only when the current has been lowered to about 0.02 mA. This non-reversible behaviour of the Josephson I-V characteristic can be explained using the resistively and capacitively shunted junction (RCSJ) model [1]. The RCSJ model takes into account effects due to the shunt resistance and capacitance that are present in real Josephson junctions. In this model, the superconducting state does not reappear on the return sweep until a certain current, called the retrapping current, is reached [4]. This retrapping current is lower than the critical current, which agrees with our I-V results.

Now, we applied various magnetic fields to see how the critical current would be affected. The results are plotted below.

Fig 8: The plots for the magnetic field dependence of the critical current for the second run (left) and the third run (right).

Our results deviate qualitatively from the Fraunhofer pattern (Fig. 3) in numerous ways. One difference is the large peak at around 2 G in the second run (left). The cause of this extra peak is unknown, but it does not appear in the plot for the third run, where we placed the dewar inside a magnetic shielding cylinder to block out external fields. Furthermore, we notice that both of our plots seem to be shifted to the left from the origin. The shift is subtle in the plot for the third run, but it is obvious in the second run; the main peak that should be at 0 G is moved to around -5 G. This shift, along with the raised minimum at around 2 G in the third run, are extremely similar to the known effects of flux trapping [5]. Flux trapping in Josephson junctions occurs due to Lenz's law when a perpendicular magnetic field is applied to the junction right as it is transitioning to the superconductive phase. This results in deviations from the expected Fraunhofer magnetic dependence pattern, including shifts and raised minima similar to our results. We were not applying any perpendicular flux to the junctions during their superconducting transitions, but there may have been stray flux generated by nearby lab equipment and the Earth's magnetic field.

Despite various mismatches, the locations of critical current minima in the plots are linear. Using MATLAB, we perform a least-squares (LSQ) fit of the magnetic field values corresponding to the nth minimum. The results are shown below.

Fig 9: Locations of critical current extrema in Fig. 8 are plotted.

The obtained slopes for the fits were and , respectively. We know that the critical current minima occur at nonzero integer multiples of the flux quantum. Thus, using our obtained slope and junction dimensions, we can solve for the magnetic flux quantum:

for the second run and

for the third run. Compared to the accepted value of , these results were off by 5 and 9 standard deviations, respectively. This is large (for a normal distribution, the probability of being 5 sigmas off from the accepted value is about 99.99994%), but this is not too surprising considering how much our magnetic field dependence plots deviated from the normal Fraunhofer pattern.

CONCLUSION

A Nb-Si-Nb Josephson junction was used to measure the DC Josephson effect. The I-V characteristics were analyzed, and the DC magnetic field dependence of the critical current was investigated. There were some dissimilarities between the obtained magnetic field dependence pattern and the expected Fraunhofer pattern. However, the overall oscillating behaviour of the critical current was successfully observed, and the locations of the minima in the pattern were linear. The flux quantum value was experimentally determined from the LSQ fit slope of the plot of magnetic fields corresponding to each minimum. Data from the second run yielded the value closest to the accepted value:

, which is 5 standard deviations off from the accepted value .

There are still numerous unanswered questions that must be addressed. In particular, future experiments should investigate possible noise and external magnetic fields interfering with the results. Laboratory equipment are sources of extra magnetic fields, and the magnetic field from Earth itself may be nontrivial since we are working with magnetic fields of a few gauss [1]. The single layer magnetic shielding used in the third run was not tall enough to cover the entire dewar; trials should be performed with larger, multilayer magnetic shielding.

ACKNOWLEDGEMENTS

This experiment would not have been possible without Professor Zimmermann and Kevin Booth. We would like to thank them for providing valuable instruction, advice and support throughout this experiment.

CITATIONS

[1] Barone A and Paterno G. Physics and Applications of the Josephson Effect. Hoboken: Wiley, 1982.

[2] Feynman R, Leighton R, and Sands M. The Feynman Lectures on Physics, Vol. III. Boston: Addison-Wesley, 1963.

[3] Tinkham M. Introduction to Superconductivity (2nd Edition). New York: McGraw-Hill, 1996.

[4] Chen Y, Fisher M, Leggett A. The return of a hysteretic Josephson junction to the zero-voltage state: I-V characteristic and quantum retrapping. J. Appl. Phys. 64: 3119, 1988.

[5] Uchida N, Enpuku K, Matsugaki Y, Tomita S, Irie F, and Yoshida K. Flux trapping in josephson tunnel junctions. J. Appl. Phys. 54: 5287, 1983.