F18_Josephson

Magnetic Field and Temperature Dependence of Critical Current for Nb-Si-Nb Josephson Junction

Chi Feng & Yuya Teshima

University of Minnesota, Twin Cities

Methods of Experimental Physics - Fall 2018

Abstract

The magnetic field and the temperature dependence of the critical current for the Niobium (Nb-Si-Nb) Josephson junction was measured in this experiment, as well as its I-V characteristic curve. The results of I-V characteristic curves indicated that there was hysteresis in the system, and the magnetic field dependence curves have horizontal and vertical shifts compared to the theoretical diffraction pattern. A difference between the measured and theoretical temperature dependence curve was observed as well.

Introduction

A Josephson junction is composed of two superconductors and a thin layer of insulator between them. Once the junction is in its superconducting state, a supercurrent flowing through the junction can be observed. This effect, discovered by Brian Josephson in 1962, is known as the Josephson effect.

The superconducting state of the junction will not be maintained if a large enough DC current is applied. The maximum current value can be applied, while the superconducting state is still maintained, is called the critical current value.ψ

The goal of this experiment is to study the magnetic field and the temperature dependence of the critical current in a Nb-Si-Nb Josephson junction.

Theory

FIG. 1: Josephson junction diagram. Light gray area are superconductors, which are in our case niobium. They are separated by a thin layer of amorphous silicone insulator, which is shown as a dark gray area. Shaded areas indicate London penetration depth of niobium; the effective length that a magnetic field penetrates.

I-V Characteristic

The constitutive relation of the Josephson effect can be written as following:

Here J is the density of supercurrent, and ϕ = θ₂ -θ₁is the phase difference between two superconductors. Each superconductor is assumed to be in

state ψ₁and state ψ₂. Applying the time-dependent Schrödinger equation to the two states, the phase difference ϕ can be written as

and so

Here ϕ₀ is the phase difference at t=0, and q is a pair of electrons, which is 2e.

When V0 = 0, the phase difference results from equation above be constant not necessarily zero. Therefore, J0 can flow through the barrier with zero voltage drop. This effect is called the DC Josephson effect. Without the voltage, the Josephson current across the junction is:

Magnetic Field Dependence of Critical Current

FIG. 2: Theoretical magnetic field dependence of critical current. Each maximum indicates the maximum Josephson current (critical current) at corresponding magnetic field.

When an external parallel magnetic field is applied to the junction, the critical current changes in following way, depending on the applied magnetic field:

Here I_c is the critical current, Φ is the magnetic flux through the junction, and Φ₀is a constant called flux quantum.

Temperature Dependence of Critical Current

FIG. 3: Theoretical temperature dependence of critical current curve for Nb-Si-Nb junction.

On the other hand, the temperature of the system can affect the critical current as well, described by the following equation:

Here RN is the normal resistance (namely, the resistance of the Josephson junction in normal, or non-superconducting state) and Δ(T) is the energy gap depending on the temperature. The expression then is normalized to make it dimensionless.

FIG. 4: Designed Main Circuit Diagram

The junction is on a chip, which is similar to the schematic diagram below.

Experimental Setup

The main circuit used for this experiment is shown in the following diagram.

FIG. 5: Schematic Diagram of the Chip with Josephson Junctions

Here, Josephson junctions appear at each cross-section of two diagonal niobium strips, shown as blue squares in Figure 2. To connect the junction, four indium joints were made on the corresponding niobium strips' ends (yellow squares in the figure), and indium wires were used to connect the junction to the circuit.

The shaded part in the main circuit diagram was mounted to the end of the cryostat, shown in Figure 3 below.

FIG. 6: Schematic Diagram of the Cryostat

The thermometer used in this experiment is a 1/10-watt resistor made by Allen-Bradley, specially designed for working under very low temperature. The heater is another specially designed resistor for low temperature made by KOA Speer company. A vacuum can was used to provide insulation. To measure the magnetic field dependence, a solenoid made of niobium-titanium wires (superconducting critical temperature about 10 K) was calibrated and used for providing parallel external magnetic field to the junction.

During the experiment, the cryostat was inserted into a Cryofab dewar shown below.

FIG. 7: Schematic Diagram of the Cryofab Dewar

Liquid nitrogen was used to cool down the system to 77 K. After a night of cooling down by liquid nitrogen, liquid helium was used for further cooling to 4.2 K. All of the measurements were done when the junction begun to show its superconductivity.

Data and Analysis

I-V Characteristic

FIG. 8: I-V characteristics observed from the first run (left) and the second run (right) at about 4.2 K. Hysteresis can be observed from both characteristics; the vertical lines (superconducting state) is branching out at the middle of the lines. Arrows indicate the direction of the flow of the current applied.

Fig 6 above shows the I-V characteristic curve of the Nb- Si-Nb junction observed with the oscilloscope from the first run. The critical current from the first-run I-V characteristic above was measured to be 2.10 ± 0.01mA . For the second run, the critical current was measured to be 1.10 ± 0.01mA, which is about twice less than the value measured in the first run.

Both the I-V characteristics show a hysteresis; the vertical line (superconducting state) is branching out at the middle of the line.

The arrows show the flow of the current across the junction. A triangular wave was supplied to the junction, so as the current increases from 0 to the peak, the current in the junction move from the superconducting state (a vertical line along y-axis) to the normal state (behaving as Ohm’s law). When the current supplied reaches the maximum, it goes back to the middle of the superconducting state, not to the point of the critical current, but to the middle of the superconducting state.

Magnetic Field Dependence of Critical Current

FIG. 9: Magnetic filed dependence of critical current for the first run (blue data) and the second run (red data) at 4.2 K. The maximum critical current at zero field for the second run is shifted to left or right, or collapsed. This might be due to a change in the pre-amplifier in the second run.

The magnetic field dependence of the critical current is shown in Fig 9 above. As shown in Fig 8, the first run has the maximum critical current at zero field, but for the second run it appears to be shifted to left or right, or collapsed from the curve and instead it has a minimum at zero field. We had changed the pre-amplifier from PAR Model 113 to Stanford Research SR560 between the first fun and the second run, so this might be caused the problem shown in the figure.

Both of the diffraction patterns did not reach zero critical current. This offset was considered to be a result from a summation of different diffraction patterns with various frequency.

Temperature Dependence of Critical Current

FIG. 10: Temperature dependence of critical current. The blue curve is the theoretical temperature dependence curve, and the red points are experimental data points. The data points came from the configuration in the second run, and they were deviated from the theoretical curve.

The experimental data points of the temperature dependence of the critical current deviated from the theoretical curve. The gap in the experimental data at T/T_c = 0.6 was happened when we changed the temperature control method from the heater to the increase by natural process.

The mismatch in the temperature dependence curve might come from the moisture inside the dewar and the change in thermodynamic cycles.

Reference

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