Understanding Josephson Junctions and How to Make One

Applications requiring precise manipulation of current - at the electron level - leave us wondering if there could be a device capable of fine-tuning electron flow. For instance, a transmon qubit used in superconducting quantum computing would require a high level of control over the electrons that pass through it [1]. Another example can be found in magnetometers used to design superconducting quantum interference devices (SQUIDS). Josephson junctions address this opportunity of fine control by leveraging superconducting properties exhibited by metals and won Brian Josephson (after whom the junction is named) a Nobel prize alongside Leo Esaki and Ivar Gaiver in 1973 [2].

Josephson Junctions

A Josephson junction is a device that allows for electron tunnelling by way of 2 superconductors separated by a barrier [3].

Broadly, there are 3 configurations for the junction:

1. S-I-S refers to 2 superconductors separated by an insulating material.

2. S-N-S refers to 2 superconductors separated by a non-superconducting metal.

3. S-c-S refers to 2 superconductors separated by a physical constriction, which is a gap of space between superconducting surfaces.

In all cases, the non-superconducting region is a weak link and serves as a barrier which electrons must tunnel through to produce a current, referred to as “supercurrent.”

Josephson’s Effect

The Josephson junction is named after Brian Josephson, who theorised that the phase difference between two superconductors should lead to a current flow even in a zero voltage regime. Note that we take phase as a degree of freedom in a superconductor but since it cannot be measured, rather only a phase difference can be measured, we interpret phase difference as the difference in the phases of the applied current and the critical current of the system [4, 5]. This phenomenon is known as the Josephson effect.

This last detail is what makes the Josephson effect so interesting: previously, Giaver performed measurements of energy gaps in ionised superconductors by measuring voltage differences. He observed the flow of electrons when he measured 0 voltage and presumed that it was experimental error. Instead, Josephson proposed that if two systems can exchange electrons - that is, if electrons can tunnel through a superconducting medium - then the phase difference between these should indicate the direction of current flow [5, 6].

What is superconductivity

Superconductivity is a phenomenon observed in conductors, primarily in metals, where the material’s electrical resistance is negligible. This is achieved by cooling the conducting material to its critical temperature, near absolute zero, at which point it undergoes a state transition.

The resulting superconducting state allows for the flow of electrons without loss of energy and thus favours high-precision applications that deal with very small current flows. For example, Wang et al. found that LiFeAs compounds displayed superconductivity properties up to 18K [7].

What are Cooper Pairs

Leon Coopper proposed the idea that in a superconductor, the electrons attract each other just enough to overcome coulombic repulsion and form pairs due to the ionic nature of molecules in the crystal lattice of the superconductor. This phenomenon occurs at the critical temperature of the material, of course. The small attraction between electrons allows them to bind and move freely through the superconductor, without resistance [8].

Tying this back to Josephson junctions, Cooper pairs are used in the tunnelling between superconductors and their coherence determines the junctions’ efficacy. This is why thermal noise and stray magnetic fields have a signification impact on quantum devices. Apart from lattice impurity, these two causes disrupt the bound electrons and thus degrade the system's overall coherence. In this context, coherence refers to Cooper pairs bound together and being able to tunnel across the barrier. Decoherence introduces electric resistivity through electron scattering in the crystal lattice and thus disrupts the current of the superconductor located before the barrier.

Building a Josephson Junction

Traditionally, Josephson junctions are constructed by layering an insulator and an isolator (typically silicon oxide) between two superconductors.

The isolator is shaped to facilitate narrow access to the barrier, such that current and voltage can be probed.

Another method is proposed by a lab at Cambridge University to facilitate machining the device, whereby the number of layers in the junction is reduced in favour of carving holes to probe current and voltage across the barrier. The junction is made by layering a barrier between two superconductors. Then a gallium focus ion beam is used to create two cuts perpendicular to the barrier [9].

While the novel method yields a tetromino shape, it preserves the defining mechanism for the Josephson junction: the current must pass perpendicular to the junction.

We thus denote the crucial area of the junction as the region between the holes where an S-I-S cross-section is observed.

References

[1] T. E. Roth, R. Ma, and W. C. Chew, “An introduction to the transmon

qubit for electromagnetic engineers,” ArXiV, 2021. [Online]. Available:

https://arxiv.org/abs/2106.11352

[2] The Nobel Prize, “Brian d. Josephson,” 1973. [Online]. Available:

https://www.nobelprize.org/prizes/physics/1973/josephson/lecture

[3] B. Josephson, “Possible new effects in superconductive tunnelling,” Physics

Letters, vol. 1, 1962.

[4] (2015) Superconductivity: Professor Brian Josephson. Youtube. [Online].

Available: https://www.youtube.com/watch?v=cnZ6exn2CkE

[5] T. Orlando, “Lecture 11: Basic Josephson Junctions, ” MIT, 2003.

[6] D. Koelle, “Basic Properties of Josephson Junctions,” EKUT, 2018

[7] X. Wang, Q. Liu, et al., “The superconductivity at 18 K in LiFeAs system,” Solid State Communications, 2008. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0038109808005851

[8] L. Cooper, “Bound Electron Pairs in a Degenerate Fermi Gas,” Physical Review, vol. 104, 1956.

[9] (2015) Superconductivity: fabricating special Josephson Junctions. Youtube. [Online]. Available: https://www.youtube.com/watch?v=-0M6g2kjdCw