The Josephson Effect

Superconducting devices are becoming a central component in a variety of new technologies. Selected for their remarkable electronic and magnetic properties, the development of materials that enter the superconducting state at reasonable temperatures has increased their practicality. In this article, we discuss the Josephson effect and investigate its applications to modern-day physics and engineering.

Superconductivity

The electrical resistance of a superconductor diminishes upon being cooled below a critical temperature. This is accompanied by the complete expulsion of a magnetic field from the bulk of the material for some superconductors, known as the Meissner effect. These properties can be explained by the fact that pairs of electrons, not individual electrons, carry electric charge around a superconductor.

Phase Coherence

The wavefunction of superconducting charge carriers has both a magnitude and phase. When cooled into the superconducting state, there is an energy cost associated with gradients in the phase of nearby carriers. Each carrier wants to minimise its total energy and will consequently adopt the phase of the others, resulting in zero gradients and therefore zero energy penalty. The superconducting wavefunction can thus be described macroscopically with a single value of phase. This phenomenon is known as phase coherence.

The Josephson Junction

The Josephson effect can be demonstrated by placing two different superconductors together, separated by a thin layer of insulator, usually a metal-oxide. Each superconductor has its own distinct macroscopic phase, notated θ1 and θ2. Such a device is known as a Josephson junction and is displayed schematically in Figure 1.

Figure 1: Schematic diagram of the Josephson junction. Each superconductor has a unique macroscopic phase, resulting in a phase difference θ1 – θ2. The gradient in phase across the junction results in the flow of a current in the absence of an applied voltage.

By selecting two pieces of superconductor such that θ1 ≠ θ2 there is a gradient in the phase across the junction. Even in the absence of an applied potential difference, the gradient in phase results in the flow of a small DC current across the junction. The larger the phase difference, θ1 – θ2, the larger the resulting current.

It is difficult to picture how the superconducting electron pairs can propagate through the insulating layer. Theory suggests that upon entering a non-superconducting material, the bond that holds the two electrons together should be broken. In fact, electrons pass through the insulator via quantum-mechanical tunnelling.

The macroscopic wavefunctions of the two superconductors overlap, giving a non-zero probability of electrons tunnelling through the barrier between them. This also explains why the insulating layer must be thin in order to observe the effect. Too thick, and the wavefunctions on either side of the barrier will no longer overlap, preventing tunnelling from occurring.

Applications

The Josephson junction has been utilised in a number of different ways, most recently within superconducting qubits for quantum computation. The active component of a superconducting qubit is known as a SQUID. Two Josephson junctions are placed within a superconducting loop, as displayed in Figure 2.

Figure 2: Diagram of the SQUID. Small magnetic fields include a circulating current in the device. For the top half of the loop, the induced current opposes the input current, whereas for the bottom half it flows with the input current. Small changes in currents can be detected and the size of the field inferred.

The SQUID can be used to detect tiny changes in nearby magnetic fields. Field lines passing through the device induce a current that circulates the device. The induced current is in the same direction as the input current for one of the loop’s branches and in the opposite direction for the other.

A small change in a nearby field will eventually lead to changes in the superconducting phase. This change in phase will result in a change in the current flowing across the junctions – as discussed, the junction current depends on the junction phase difference. These changes in current can be detected and turn out to be incredibly sensitive to changes in field strength.

As well as quantum computation, SQUIDs have been used in biomagnetic measurements, such as detecting tiny variations in the neural magnetic field resulting from the firing of groups of neurons.

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