S18_Josephson Junction

Josephson Junction

Benjamin Bauer & Zachary Williams

Introduction

The Josephson effect is the zero resistance flow of current through an insulating layer pressed between two superconductors. It was predicted in 1962 by Brian David Josephson, who theorized that the effect was caused by the tunneling of superconducting electron pairs. This effect takes place through what is called a Josephson junction, two superconducting wires separated by a thin insulating barrier. In this experiment we mapped the Current-Voltage (I-V) characteristics of a Josephson junction using an applied current across the junction, as well as observed the effects of a magnetic field on the junction. The junctions we dealt with were made of niobium due to its high superconducting transition temperature of 9.3K. Josephson junctions are crucial to superconducting quantum computing as they form flux qubits and phase qubits, and can be made into SQUIDs (superconducting quantum interference device) used to measure magnetic fields in devices such as MRI scanners.

Figure 1: A basic Josephson junction

Theory

In superconductive materials, electrons become paired due to electron-phonon interaction. These are known as Cooper pairs, which have a minimum energy larger than the thermal energy of the lattice of material they are in, allowing them to behave like a superfluid and carry zero-resistance current. In a Josephson junction with a voltage difference across the insulator, there is a current density across the junction given by

with zero voltage, this results in a current across the junction of

This equation allows for zero-voltage current up to a critical current, above which the Cooper pairs break apart as they tunnel creating Bogoliubov quasi-particles which encounter resistance.

Applying a magnetic field perpendicular to the junction as shown in figure 2,

Figure 2: Application of magnetic field onto junction, the London penetration depth is a property of the material.

the current becomes

and so

From this we would expect to see a zero-voltage current up to a critical current with the critical current having a diffraction pattern shown in figure 3.

Figure 3: Expected effect of magnetic field on critical current.

Apparatus/Procedure

To observe the Josephson effect, we measure the I-V characteristic of the junction with an applied AC current as shown in figure 4.

Figure 4: We apply a current across the junction and measure the voltage.

Our niobium junction is one of 9 junctions in an array on a chip, shown in figure 5. It is taped to a mount and leads are attached using indium. We estimate that our specific junction has a size 4.25*10^-8 cm^2 and have observed "bubbles" beneath the surface which we think is dirtiness left in during production.

Figure 5: Chip holding the array of junctions mounted.

The mount is then attached to a cryostat and it encased in a solenoid which will produce the magnetic field. The cryostat is inserted into a Cryofab dewar which is cooled to 4K with an outer bath of liquid nitrogen and an inner bath of liquid helium.

Figure 6: Cryostat and Cryofab dewar used to cool the junction and take measurements.

Once the junction is cooled to superconducting temperatures, we measure the I-V characteristic using an oscilloscope and vary the magnetic field to observe the diffraction pattern.

Data/Analysis

We observed the characteristic shown in figure 7, where the y-axis is current obtained by dividing the graph value by 10,000 Ohms for the graph on the left and 1,000 Ohms for the graph on the right, and the x-axis is the voltage obtained by dividing the graph value by 10 (which comes from an amplifier). The right graph is simply a zoom into the center of the left graph. The superconducting energy gap is observed in the left graph at about 30V.

Figure 7: Observed I-V characteristic, the y-axis is current and the x-axis is voltage.

Taking the critical current as the maximum current at zero voltage, the magnetic field dependence is plotted in figure 8, and the zero-points, or minimums, are plotted and fitted to integer steps. The horizontal and vertical shifts from zero can be explained with small offsets in our current supply and measurement, and we estimate the irregularities in the curves come from dirtiness within our junction.

Figure 8: Magnetic field dependence of critical current on left, minimums plotted against integer steps on right.

From the maximum value of the plot we have a critical current

and from the spacing of the zero-points of the diffraction pattern we are able to calculate

where the large systematic uncertainty comes from our lack of knowledge of the manufacturing of our junction.

Conclusion

The produced critical current-magnetic field relationship has irregularities due possibly to the dirtiness observed below the surface of the chip holding the junctions. Regardless of these irregularities and the small critical currents, the junction produced a reasonable value for the flux quantum, which is accepted as 2.07* 10^-7 G*cm^2. For future experiments, accurate knowledge of the size of the junction and access to a clean junction is recommended.

References

[1] Kittel, C., Introduction to Solid State Physics, 6th Ed., Wiley., 1986.

[2] Barone, A., & Paterno, G., Physics and Applications of the Josephson Effect. Wiley. 1982.