S17_JosephsonJunction

Investigating Josephson Junctions to Determine the Flux Quantum

Maxwell Yurs and Joe Eix

University of Minnesota

Introduction:

The Josephson effect describes the process in which a supercurrent is produced across a Josephson junction which consists of two superconductors separated by a thin insulating barrier. Tunneling cooper pairs, which are electrons bound due to the superconductor, give rise to the supercurrent. When applying low currents, no voltage drop will occur across the junction which is denoted as the DC Josephson effect. Applying a finite voltage instead results in an oscillating supercurrent called the AC Josephson effect. Only the DC effect was investigated in this experiment though. Chips of crossed niobium strips commercially produced for Professor Goldman's group were utilized in this experiment. A double walled dewar was used to cool the chips using liquid He to cool below niobium's critical temperature of 9.3° K. Magnetic fields affect the Josephson effect by altering the maximum current the junction can sustain with zero theoretical voltage drop. This change has minima when the product of the magnetic field magnitude and junction attributes are whole multiples of the flux quantum. The flux quantum can be determined from these minima.

Theory:

Josephson junctions are two superconductors separated by a thin barrier. Because of superconductivity principles, the Cooper pair charge carriers in either superconductor share the same wavefunction. If the thickness of the barrier separating the superconductors is thin enough, the charge carrier wavefunctions can penetrate across. Formalized, this relationship is when the barrier thickness is smaller than the London penetration depth. With this relationship, the wavefunctions on either superconductor become coupled, allowing for the tunneling of Cooper pairs across the resistive barrier with no voltage drop. This tunneling is limited up to maximum currents, called the critical current, governed by the resistance of the barrier and the phase difference between the coupled wavefunctions. This is expressed by the equation:

Where J is the current density, Jo is the critical current density, and theta is the phase difference between the superconducting wavefunctions. The phase difference is affected by the presence of a magnetic field, and is proportional to the magnetic flux in the junction. This relationship is:

Where theta_mag is the phase difference in the presence of the field, d is the penetration depth into either side of the junction, B is the magnetic field, and z is the coordinate perpendicular to the field and along the length of the junction (see figure 1). By inputting this phase relation into the relation for current density, the result is that current density changes with the z coordinate. Integrating the current density over the area of the chip gives the critical current, and reveals minima in critical current for specific magnetic fields. For a square junction, this relationship is:

Where I is the critical current, Io is the zero field critical current, Phi is B*d*L from figure 1, and phi_0 is the flux quantum. Minima in critical current occur when phi is a multiple of phi_0, (see figure 2).

Figure 1: The upper and lower superconductors separated by a barrier of thickness t. The magnetic field is out of the page along the positive y axis. L is the width of the junction. The dimension lamda is the London penetration depth.

Figure 2: A Fraunhofer-like pattern resulting from plotting the critical current vs magnetic field. Ic corresponds to I, and Ic0 corresponds to I0. [2]

Experimental Apparatus and Procedure:

The chips consist of crossed niobium strips separated by a thin layer of amorphous silicon. Two chips were cut from the whole silicon wafer with the help of Ilana Percher.

Figure 3: The Josephson junction which was investigated exists at the intersection of the diagonal strips. The center junction was used because its connection pads were the easiest to connect to.

The chips were mounted with varnish onto a raised copper face with a circuit board that is flush and surrounds the face. Since the chips are fragile, a "col-solder" technique using indium was employed to connect the contact pads of the chips to soldering posts in the circuit board. The posts provide a more robust point for connecting to the central wires run down through the dewar to the cryostat containing the chip and liquid helium. Insulated wire was used for this connection to avoid short circuits. A breakout box created by a past MXP group separates the wires of the cryostat and has BNC connections so that shielded cable can be used when connecting instruments. This breakout box also served as the common ground for the experiment. An Agilent 3410a multimeter was used to measure the potential across the junctions while a current was being applied using a Keithley 224 programmable current source. Both the multimeter and current source were controlled using a LabVIEW program.

The dewar in this experiment has two chambers, the outer for liquid nitrogen and the inner for liquid helium. Layering liquid nitrogen provides insulation for the liquid helium from room temperature, so it can reach temperatures below niobium’s critical temperature of 9.3° K. Niobium must be cooled below this temperature for it to gain superconducting properties, a requirement for the junctions to function. A basic cross sectional schematic of the dewar is shown along with a basic circuit diagram for the experimental setup.

Figure 4: The left panel displays the cross section of the dewar used. Its access ports are visible showing where the coolants were transferred. The vacuum pump-out was used remove any air and replace it with gaseous helium. The right panel shows the circuit for the experiment where x is the symbol of a Josephson junction. A separate current source was used to power the solenoid used. The junction is within the solenoid in the actual setup but is shown next to it in the diagram to clearly see the separate circuits. We used a Four Wire method to measure the potential across the junction as accurately as possible.

This setup was used to complete the data collection process. A single trial began by first applying a magnetic field and allowing approximately 5 seconds for the field to stabilize and become constant. Next current was swept through the desired range of ±50 mA using the increments described above. The sweep began at the negative limit and rose to the positive limit and finally returned to the negative limit. Current applied to the solenoid was then adjusted to apply a different magnetic field and the process was repeated until the desired range in magnetic field of -7.95 to 7.08 Gauss was completed. This range was expected to contain three minima in critical current where the minima occur at multiples of 2.35 Gauss applied magnetic field. This value was calculated from the following

where d equals 88 nm and L equals 100 μm [1].

Results and Analysis

Figure 5: A typical I-V plot obtained in this experiment is shown on left. Both current sweeps are shown overlaying in good agreement. Voltage readings shown are amplified by 10. Error bars are too small to see; about 10^-4 in voltage. On right, critical current vs magnetic field is plotted. Critical currents from both directions in current axis are shown, for each current sweep. Error bars are shown but too small to see, about 5x10^-6 amps. Magnetic field effects on the junction are not evident, since at lease two minima were expected.

By examining figure 5, the critical current region is pronounced in the I-V plot. Values for positive and negative critical current were obtained for each sweep based on when the interpolated slope crossed a threshold. Based on the right plot, magnetic field dependence is not evident on this junction. This leads to the conclusion that this junction was not exhibiting Josephson behavior, but rather a different type of weak link. One concern is that the I-V characteristic does not return to Ohmic behavior at large currents.

Figure 6: On left, critical current behavior of weak link structure with two bulk superconductors separated by a superconductive cross-section [4]. Note that I-V curve does not return to Ohmic behavior. On right is shown the I-V plot from figure 5, superimposed with the warm behavior of the the junction. As is evident, the junction also does not return to Ohmic behavior.

Figure 6 showcases that the I-V behavior observed in this experiment is strikingly similar to that of another type of weak-link structure rather than a Josephson weak-link. In particular, this structure is two large superconductors separated by a small superconductive area. In the Josephson effect, I-V behavior should return to Ohmic behavior past the gap voltage, in this case around 1 mV [1]. However, this gap voltage is not evident. The similarity of this effect with the observed I-V characteristics of a the weak link structure in figure 6, combined with the lack of magnetic field dependence leads to the conclusion that the junctions used in this experiment are defective or experienced damage or aging affects.

Conclusion:

The Josephson effect was realized in a weak link structure with a consistent positive critical current of approximately 200 μA and negative critical current of approximately -280 μA for varied applied magnetic fields. The lack of magnetic field dependence combined with not returning to Ohmic behavior as dictated by theory indicates that the junction used in the experiment has degraded into a different type of weak link structure. Further investigation in literature reinforced this conclusion.

Acknowledgments:

We would like to thank Professor Zimmermann and the entire MXP staff for their guidance and assistance throughout the semester.

References:

[1] Tinkham, M. (1975). Introduction to Superconductivity, 1^st Ed. “Josephson Effect and

Macroscopic Quantum Phenomena (pp. 192-230). USA: McGraw-Hill Inc.

[2] Barone, A. and Paternó, G. (1982). Physics and Applications of the Josephson Effect

(pp 9-18, ch. 13, ch. 14). USA: Wiley-Interscience.

[3] Wick, K. et al. (2015). Physics 4051 Lab Manual (pp 61). University of Minnesota:

School of Physics and Astronomy.

[4] Clarke, J. (1970). The Josephson Effect and e/h. American Journal of Physics 38,

1071.