Superconductors

Introduction

In 1908 Kammerlingh Onnes, a scientist that worked at the Leiden University, succeeded in obtaining liquid He; thank to this result, he could go on with his studies in the field of low temperatures. In particular, Onnes was interested in investigating the behaviour of electrical resistance of metals at temperatures near absolute zero. At that time it was well known that electrons were responsible for electrical conduction and that the electrical resistance of a metal decreases with decreasing temperature; nevertheless, very different theories circulated about resistance at very low temperatures: decreasing temperature it could assume very high values or remain nearly constant or gradually diminish. Onnes measured the electrical resistance of gold and platinum; then he understood that the only metal that he could obtain in an extremely pure form was mercury; so he used this metal for his measurements. What he obtained was different from each of the theories described before: at a certain temperature (4.2 K) electrical resistance fell suddenly to very low values, not distinguishable from zero, as reported in the figure. It was 1911, superconductivity was discovered.

A superconductor is a material that shows two main properties: under a certain temperature, called critical temperature (Tc), its electrical resistance falls to zero and the field lines of an external magnetic field (if the field intensity is below a critical value (Hc)) are excluded. To understand the latter property it must be kept in mind that materials can behave differently if introduced in a magnetic field: they can be for example slightly attracted (if they are paramagnetic), strongly attracted (if they are ferromagnetic) or repelled (if they are diamagnetic). Superconductors are the only example of materials that completely repel an external magnetic field; they are for this reason called perfect diamagnets. A very convincing evidence of this fundamental property of superconductors is the so called magnetic levitation: when the magnet is brought near the superconductor at room temperature nothing unexpected happens; on the contrary, when the superconductor is cooled below Tc by means of liquid nitrogen, the two objects repel each other and the magnet remains raised over the superconductor without touching it. The surprising behaviour of a superconductor within a magnetic field below Hc is well illustrated by the Meissner-Ochsenfeld effect. Actually, the magnetic field penetrates into the superconductor through a very thin layer on the material surface. The penetration thickness is called penetration depth and is indicated with λ.

Besides Tc and Hc, the other important parameter that defines the superconducting state is the critical current density (jc). The material remains in the superconducting state until the current density that goes through the volume remains below a critical value. A superconductive state can the be defined, that sets in below Hc, Tc and jc. The critical values are different, according to the compound. Within this state the material is a superconductor, outside (i.e. above Tc and/or Hc and jc) it is a normal conductor (see figure). Moreover, superconducting materials can be divided into type I and II superconductors, depending on the existence of one or two critical values of the magnetic field.

What makes superconductors so extraordinary? Every normal conductor is characterized by a certain value of electrical resistance, that, as described, depends on temperature, as well as on the sample size: the lower the resistance value, the better the conductivity properties of the material. Electrical resistance is a consequence of the interaction between electrons (responsible for electrical conduction) and crystal lattice: the conduction electrons, accelerated by the electric field produced by a voltage between two points, transfer a part of their energy to the lattice. This energy is then dissipated and changed into heat (Joule effect). A superconductor is on the contrary, at a first approximation, a dissipation-free conductor.

In the first years after the discovery of superconductivity a huge number of elements were found superconducting if properly cooled and eventually under pressure; similarly, many metallic alloys can become superconducting. Why is a wide use of superconducting elements or alloys, for example for electrical energy transportation, so difficult? The discovery of superconductivity goes back to the first years of the last century, but applications are still far away from the everyday life. When speaking about superconducting elements or alloys, the values of Tc, Hc and jc must be kept in mind. If we analyze Tc of elements and alloys (see table), we can notice that these temperatures are very difficult to achieve because extremely low: cooling an object down to few Kelvin implies the use of liquid He, that is very expensive. Only below Tc superconductors show the disappearance of electrical resistance and the perfect diamagnetism.

After the first enthusiastic decades that followed the discovery of superconductivity, it seemed that this phenomenon, although very interesting, had to be confined to the laboratories and considered no more than a scientific strangeness: the critical temperatures achieved were too low for any application; moreover, the commonly accepted theory that explained superconductivity (the BCS theory) predicted that Tc’s can not overcome 30 K. But a new discovery reinvigorated researches in this field: high temperature superconductors (HTSC). In the Eighties of last century Alexander Müller and his pupil Georg Bednorz worked in the IBM laboratories in Zurich at the search for higher temperature superconductivity (at that time the highest Tc reached was 23 K) in ceramic systems. In 1985 they succeeded in obtaining a superconductive transition at 35 K in the Ba-La-Cu-O ceramic system. It was a striking discovery: from 1911 to 1985 Tc had raised from 4 K (mercury) to 23 K (Nb3Ge); higher Tc’s were thought unachievable, while now such a high Tc was found in totally different systems! Because of the extraordinariness of this discovery (Bednorz and Müller were jointly awarded the Nobel prize in physics in 1987), they presented their results in a scientific paper cautiously entitled: “Possible High Tc superconductivity in the Ba-La-Cu-O System” (Zeitschrift für Physik B 64 (1986) 189-193).

In the first years after this discovery the announcements of always higher critical temperatures followed on; YBCO (YBa2Cu3O7), 92 K (see the crystal structure in the figure); BSCCO (Bi2Sr2Ca2Cu3O10), 110 K; mercurocuprates (HgBa2Ca2Cu3Ox), 133 K. But, apart from the obtainment of always higher Tc’s (that do not always correspond to a better applicability of the material, as also other parameters have to be taken into account), what is very important is the achievement of Tc’s higher than the N2 boiling point (77 K): the possibility of using liquid N2, much cheaper and more easily obtainable than liquid He, made more concrete the applications of superconductivity.

Although HTSC are characterized by chemical formulae at a first sight rather complex, they have some common features: even if today, 25 years after their discovery, the superconductive mechanism of HTSC is still not completely clear, a huge number of new ceramic superconductors has been synthesized by analogy and subsequent substitutions. More recently new superconductors have been discovered: copper-based, as well copper-free compounds are nowadays studied.

There are many different possible applications for superconductors, but the most popular and important are two. The first one is related to high field magnets: in order to understand the mechanism of these devices, it must be kept in mind that a magnetic field is generated by a flowing electrical current through a conductor and that the intensity of the field generated is proportional to the current density. Superconductors, as described, are dissipation-free conductors; they can tolerate a current density much higher than a normal conductor, and then are ideal candidates for high field magnets. Nowadays the most commonly used superconductors for this application are still the “old” ones, such as NbTi e Nb3Sn. The production costs are high, as the magnet must always remain at a temperature below Tc.



The other and well known application is transportation based on magnetic levitation. Different technologies can be used in maglev (magnetic levitation trains), but the one using superconductivity is based on the repulsion between a superconducting material and a magnetic field, if the latter does not exceed Hc. In JR-Maglev, the Japanese train that reached 581 km/h (the highest speed reached by terrestrial means of transport), magnets are set along the guideways, while the trains are provided with superconducting coils cooled below Tc. This way the train can run floating about 10 cm over the guideway and experience only the friction caused by air. A miniature of the maglev train basing on superconductive technology can be seen in this video.