In future, superconducting nanoscale components may be important in electronics applications such as supercomputers. A major step will involve the development of three-terminal devices - superconducting transistors. Experimentally these are beginning to see the light. To model such small devices one can often use simple "textbook" quantum mechanics to describe the ballistic wave-like charge-carrier transport transport. These superconducting quantum devices bridge the gap between basic research and advanced technical applications.
When I was a child I used to go around to the local radio dealers and collect old radio receivers. This was in the 1950's, and since the radio equipment itself was old you can imagine what it sometimes looked like. Young Edison and Marconi would probably have felt at home. The radio tubes did more for illumination than communication. Little did I know that I would be part of the electronic revolution. During my first sabbatical in the USA 1978/79 I first found Radio Shack and then Ohio Scientific. This was only a few years after the personal computer was born - the Imsai Altair - programmed by front panel switches. However, the Ohio Scientific computer had a keyboard, a 1 MHz 6502 microprocessor and an enormous memory of 8 Kbyte static RAM in 1 Kbyte chips. We used to run the game of Moonlander, adding quite a few new craters to the face of the moon. Then came Commodore and Apple I and II and Macintosh and the IBM PC. And now we sneer at 100 MHz processors and 1 Mbyte memory chips because we can have 500 MHz processors and 64 Mbyte memory chips!!
What made this development possible during the last 20 years? From a technological point of view, one obvious answer is the transition from microelectronics to the submicron scale of components which allows dense packing, high-frequency clocking and complex functions on single chips. This in turn was made possible by epitaxial (layer-by-layer) methods for materials fabrication, producing high mobility semiconductor heterostructures. A landmark was the development of the Esaki diode at IBM around 1970 . Although one often talks about microelectronics, it is really submicron electronics that counts today. And, in fact, by making the components still smaller we are now entering the world of nanoelectronics, where quantum phenomena rule. Conventional transistors will no longer work properly because electrons may diffuse or tunnel between electrodes and gates in uncontrolled ways. To this we must add the problem of heating when we pack all these components together, and then there is the problem of connection lines. Sounds like a good idea to go over to quantum devices and make it all superconducting!
For a long time, quantum electronics has been a well known concept. However, it has usually been associated with laser physics, e.g. solid state lasers. In other words, the quantum phenomena have involved light. In nanoelectonics, electrons themselves can be propagated as waves through electronic wave guides. Materials built up with MBE (molecular beam epitaxy) can be made so free from impurities and defects that the electron mean free path is larger than the device: the electrons can move ballistically - like bullets - through the structure without collisions. The current can then be controlled via potential barriers which reflect part of these waves - Quantum Field Effect Transistor. Here is where "simple" textbook quantum mechanics suddenly becomes useful in practical enginering of advanced semiconductor material for advanced applications. A famous recent example is the quantum well injection laser .
Progress in superconducting electronics presently develops along two tracks. One is connected with high-temperature superconductors - HTS - which permits superconducting devices above 77 K using LN2 (liquid nitrogen) as a cooling medium. This development started 1986/87 with the discovery of HTS [3,4] (Nobel prize to Bednorz and Mller 1987) and is largely based on thin-film technology. It has already become competitive in specialized scientific electronic devices. The other track is connected with the "conventional" approach using low-temperature superconductors (LTS) such as niobium metal (Nb) combined with the latest technology of MBE fabricated semiconductor heterostructures. For about ten years there have been strong efforts to control Josephson supercurrent in superconducting junctions via a gate - three-terminal device - in order to construct a superconducting transistor - the missing element in superconducting electronics. A recent successful approach  using LTS is based on the technique for fabricating HEMT structures (High Electron Mobility Transistor) used for FET (Field Effect Transistor) devices. One then builds up a GaAs/InGaAs/InAs based semiconductor layered structure using MBE, dopes some layers with aluminium (Al), then adds superconducting leads of niobium metal and finally a gate (Al) on top. The structure is shown in Fig. 1. The resulting device consists of two
Figure 1. Superconducting-semiconducting-superconducting three-terminal device  - JOFET - Josephson Field Effect Transistor.
superconducting Nb leads (S) connected by a very thin (4 nm) InAs metallic sheet of electrons - a so called two-dimensional electron gas - 2DEG. The S-2DEG-S device functions as a Josephson junction: under proper conditions it will carry dc and ac Josephson supercurrents. This is demonstrated in Fig. 2, which shows the I-V characteristic of the device as a function of the gate voltage Vg (the third terminal providing transistor action, i.e. control of the (super)current).
Figure 2. Current-voltage (I-V) characteristics of the S-2DEG-S device in Fig. 1 as a function of gate voltage Vg .
Figure 3. Measured critical current Ic and normal resistance RN as functions of gate voltage Vg . The measured critical current Ic in Fig. 2 (the value of the current at V=0) versus the gate voltage Vg is presented in Fig. 3. Via the gate, the critical supercurrent can be continuously varied down to zero - the device can work in principle as an amplifier or a swithch - a JOFET - Josephson Field Effect Transistor.
The beautiful results in Figs. 2 and 3 can be qualitatively understood in terms of a gate field effect on the the transport of normal electrons through the 2DEG part of the S- 2DEG-S structure. Computationally, however, the results have not yet been reproduced, either qualitatively or quantitatively! However, we are working on it, and I have no doubt that we will succeed, probably sooner than later. I will not go into any kind of detailed explanation in this article - suffice it to say that one works with the so called Bogoliubov-de Gennes equation, which is an extension of the Schrdinger equation to treating superconducting systems within the framework of BCS theory (Bardeen-Cooper-Schrieffer; Nobel prize 1972). Our approach is described in some detail in a number of recent publications [6-9]. Much to our surprise - the BCS theory of superconductivity is forty years old - we have discovered lots of fascinating new things when analyzing models of superconducting junctions and devices based on new types of structures, like S-2DEG-S, SIS tunnel junctions (break junctions) and intrinsic Josephson junctions in high-Tc materials like BiSrCaCuO . For example, we have found a Giant Josephson effect  in SIS tunnel junctions which we hope will be experimentally verified before too long. We have explained the subgap structure in the I- V characteristic of SIS tunnel junctions , and are presently discovering fascinating effects in Josephson junctions with resonant localized states buried in the tunnel barrier . Finally, we are now beginning to model three-terminal superconducting devices in order to try to explain how to control Josephson current and I-V characteristics in real devices (Figs. 1- 3) [5,6,9].
When we apply for grant money and try to impress the grant agencies we use grand sentences like: "Controlling Supercurrent: Theory and Simulation of Superconducting Nanoscale Multiterminal Devices for Superconducting Electronics". We will no doubt succeed in providing adquate theory and modelling for designing superconducting transistors. However, how soon superconducting electronics will be a technological and commercial success is an open question. Most likely there will be no commercial breakthrough for superconducting electronics - even in advanced products like supercomputers - before conventional semiconductor technology hits the wall. And that may take a long time - decades . In the meantime we will continue having fun with basic and applied research, while trying to convince Industry, TFR, NUTEK, the media and the taxpayers that we are USEFUL.
Dr. Hideaki Takayanagi, NTT Basic Research Laboratories, Atsugi-shi, Japan, is gratefully acknowledged for many stimulating exchanges. The work at CTH is partly done within the framework of the NUTEK/NFR Interdisciplinary Consortia in Materials Science and Materials Technology - No 11, Superconducting Materials, and with support from TFR, KVA and the European Commission.
 L. Esaki and R. Tsu, IBM J. Res. Develop. 14, 61 (1970).
 J. Faist et al., Science 264, 553 (1994).
 J.G. Bednorz and K.A. Mller, Z. Phys. B 64, 189 (1986).
 M.K. Wu et al., Phys. Rev. Lett. 58, 908 (1987).
 H. Takayanagi and T. Akazaki, Jpn. J. Appl. Phys. 34, 6977 (1995).
 G. Wendin and V. Shumeiko, Phys. Rev. B 53, R6006 (1996).
 E. Bratus', V. Shumeiko and G. Wendin, Phys. Rev. Lett. 74, 2110 (1995).
 P. Samuelsson, Master's thesis, CTH, School of Physics and Physics Engineering, 1996.
 G. Johansson, V. Shumeiko, E. Bratus', and G. Wendin, to be published.
 A. Yurgens, D. Winkler, N. Zavaritsky and T. Claeson, Phys. Rev. 53, R8887 (1996).
 This raises a question: if basic and applied university research will only be commercially exploitable in 10-20 years, does it have industrial relevance now? And who is to decide? Should one really require industry to be serious partners when trying to build foundations for new technologies - enabling technologies?
For more information contact
Bitr. professor Gran Wendin
Department of Applied Physics, CTH/GU
412 96 Gteborg