Introductory Notes on the Josephson Effect: Main Concepts and Phenomenology

Josephson predicted the existence of tunnel currents carried by Cooper pairs between two superconductors SR and SL separated by a thin (typically about 1 nm) insulating layer I [1], and paved the way to the study of a series of interesting phenomena associated with this coherent flow of Cooper pair currents [2, 3]. The whole story from the first tunnel Josephson junctions in the 1960ies using soft superconductors as Sn, In, Pb, and thermal oxidation for the barrier, and the subsequent “lead-alloy technology” with the first self-limiting sputter-oxidation process, to the more mature class of devices based on “rigid” superconductors as Nb, is perfectly accounted by the two main textbooks published in the 1980ies by Barone and Paternó [2] and Likharev [3], respectively. Artificial barriers replacing Nb oxide barriers were the key towards the development of the Nb technology. Al revealed as the perfect solution forming a natural, self-limiting, high quality, insulating oxide [4]. Other rigid superconductors were NbN, Nb3Sn, V3Si and Nb3Ge. All of them needed artificial barriers. From the historical point of view, the use of rigid superconductors had definitely overcome some problems of stability in thermal cycling of lead-alloy based junctions. A detailed recent account on the history of the first developments of the Josephson junctions is also given in [5]. It was not only the first search of suitable novel materials and barriers, but also of the appropriate processing techniques and layouts [2, 3, 6–8]. In the 1980ies the integrated thin film Superconducting QUantum Interference Device (SQUID) was introduced [9]. Many junctions were integrated with thin film resistors and thin film transmission-line interconnections into complex, monolithic, integrated circuits (ICs). The higher critical current density (Jc) leads to the necessity of reducing the area of the junctions to meet requirements on junction impedance, promoting special geometry such as edge-type junction or e-beam lithography in sandwich or planar layout. The technology of NbN was the first attempt to increase operating temperature of Josephson junctions [10]. Since early times it was clear that the development of superconducting devices based on the Josephson effect needed to proceed on three levels: basic physics, device and circuit innovation, and materials science and processing development. The impact of high critical temperature superconductors (HTS) was also impressive for the development of activities on Josephson devices [11–14]. It was amazing not only for the opening of new horizons in solid state physics but also for the development of novel notions and ideas in superconducting electronics, possibly operating at higher temperatures. HTS gave clear awareness of a new era where a more indissoluble link between superconductivity and material science clearly appeared. All unconventional materials after HTS have followed the same conceptual and experimental workflow to codify their unconventional phenomenology, and specifically also those notions that have been helpful for the realization of a Josephson device. This obviously includes innovative methods of building barriers in intrinsically non homogeneous materials. In the meanwhile the advent of mesoscopic physics also in superconducting systems was changing some conceptual paradigms on how to approach the problem of coherent transport in superconducting junctions, and nanotechnologies started offering new experimental tools to build completely new families of devices. The modern era of Josephson devices is thus strongly influenced by the combined continuous progress in material science and nanotechnologies applied to superconductivity. These aspects are tightly connected. Progress in material science means newmaterials and newsuperconductors, and novel abilities in building interfaces and in the precise control of heterostructure in the growth process. Also barriers of tunnel junctions are designed and fabricated with unprecedented precision, opening the route tomore performing devices even for technologies based on well established low critical temperature superconductors (LTS). Advances in nanotechnologies applied to superconductivity is a necessary tool towards several material science solutions, scaling barriers and interfaces, handling pre-built barriers as for instance nanowires (NWs) and flakes. Hybrid junctions are an obvious consequence of the combined progress of material science and nanotechnology. In conclusions, we have never had so many different families of superconducting materials and so many different types of Josephson junctions as nowadays, with so many open questions on their nature and ultimate limits of their performances. Part of their future depends on the ability of combining the unique features and advantages of Josephson devices with the functionalities of the barriers.