Introduction

In 1962, Welsh theoretical physicist Brian David Josephson made several predictions about the behavior of superconductors separated by a sufficiently thin (~20 Å) [1] weak link, which could be an insulator, a normal metal made weakly superconducting by proximity, or a narrow constriction of the superconducting material itself. The superconductors and the weak link form what’s known as a Josephson junction. The most remarkable of Josephson’s predictions was that current would flow through the junction in the absence of an applied voltage. Today, Josephson junctions have a variety of applications including usage in quantum computers [2], ultra-sensitive magnetometers (known as SQUIDs) [3], and the standard definition of the Volt [4].

Ordinary, low-temperature superconductors, when below a certain material-dependent critical temperature, exhibit zero electrical resistance. This remarkable property is due largely to electron-phonon interactions within the superconductor. Essentially, two conduction electrons of opposite spin and with equal and opposite momenta become weakly bound as a result of this interaction and form what are known as Cooper pairs. The energy of these pairs lies below the Fermi energy of the material and thus, the solid attains a lower energy state (becomes more stable) through the formation of Cooper pairs. The minimal energy is achieved for the maximum number of pairs, which occurs when the center of mass momentum of each pair is exactly the same. The result is an effective energy gap, E_g, centered on the Fermi energy [5], between the energy of electrons in Cooper pairs and the lowest excited energy states of non-interacting electrons. This energy gap is equal to twice the binding energy, Δ, of a Cooper pair, where the binding energy is just the energy difference between electrons in a Cooper pair and two unpaired electrons. A consequence of all the conduction electrons having the same energy and moving together with the same momentum is that they can be collectively treated with a single macroscopic wavefunction [6].

The probabilistic nature of quantum mechanics led to the discovery that particles have the ability to “tunnel” through a potential barrier. The tunneling of Cooper pairs from one superconductor to another through a weak link is the source of the zero-voltage current flow predicted by Josephson, and is known as the Josephson effect [3]. When the current is below the critical current, it is constant in time, and so this phenomena is called the DC Josephson effect [5]. Although this experiment will be restricted to study of the DC Josephson effect, there is also an AC Josephson effect where, for currents larger than the critical current, a potential develops across the junction and the current will oscillate with time [5].