The history of superconductors began, essentially, with the successful liquification of helium. Dutch scientist Keike Kamerlingh Onnes liquified helium in 1908, at a temperature of just 4 K, and proceeded to use it in his study of the resistance of the metal mercury (Hg) at low temperatures. He and his team had noted, previously, the regular decrease in Hg resistance to electrical currents with decreasing temperature, but were startled to note a sudden drop to zero resistance at liquid helium temperatures. Although the technicians initially thought this reading was the fault of a short-circuit somewhere, they eventually realized that it was an accurate reading. It was eventually recognized that a variety of metals, when cooled to within a range of 4 to 20 K, displayed zero resistance to electrical current. (Nobel 14)

Unfortunately for Onnes superconductors, it was later discovered that the passage of large currents through these metal superconductors produced a large enough magnetic field to destroy the superconductivity. Lead, for instance, has a critical magnetic field threshold of only a few tenths of a tesla. Although Onnes won the 1913 Nobel Prize for physics, he, and many others, realized that both the critical temperature and magnetic field thresholds would have to be greatly raised before the superconductors would really be of any use. Because the power dissipation of wires is not only proportional to the resistance squared, but also the current, the best use of superconductors would likely be in arenas where large quantities of current need to be moved since it is in these that the power dissipation would be greatest. According to Ampere's Law, however, the larger the current put into a wire, the larger the resultant magnetic field, so this was an important consideration. (Ford 63)

Even more troubling was the fact that producing temperatures only a few degrees above absolute zero is extremely difficult, and relatively expensive. Clearly, superconductors that had higher transition temperatures (the temperature below which the substance becomes a superconductor) had to be found. Until then, superconductors were likely to remain an interesting effect, but one that was relegated to the chemist's or physicist's laboratory.   Top

It was not until 1957, however, that a successful superconductor theory was put forth. Bardeen, Cooper, and Schrieffer developed their theory, now called BCS after their initials, from an earlier theory of Leon Cooper, involving electron pairing. (Ford 64)

Cooper pairs are in essence electrons in the superconducting matrix that pair up and move together, not bumping into each other, and not scattering off of imperfections in the superconductor (as electrons do in normal conductors). Although normally electrons would repel each other, their repulsion is overcome in two different ways. First, there is a "screening" effect resulting from the motions of other electrons, which reduces the repelling force between the Cooper Pair electrons. However, the more important effect is the introduction of a charge distortion called a phonon. The idea here is that the first electron of the pair shifts the position of the ions and other electrons as it moves by, creating, in effect, a small area of positive charge. This small patch then attracts the second electron of the pair. The electrons move much more quickly (at relativistic speeds, in fact) than these phonons, however, and so by the time the second electron arrives at the positive site, the other electron is far enough ahead of it that they do not repel each other. Furthermore, the electrons of a pair can interact by exchanging phonons. (Kirtley 69)

Cooper pairs are, in essence, the BCS model. This theory, although somewhat confusing, works out well mathematically and explains the properties of low-temperature superconductors. However, it also introduces a limit of about 25 K on superconducting temperatures (Ford 64). This theory was accepted, and there the matter stood, until 1986.  Top

Initially, physicists attempted to apply the BCS theory, and especially Cooper Pairs, to high-temperature superconductors, but most were quickly convinced that at least some modifications were necessary. In low-temperature superconductors, the first electron of the pair essentially behaves as if its motion were independent of anything else going on in the material. However, in high-temperature superconductors, the vibrations of the solid lattice are more energetic, and interactions between non-paired electrons are stronger. (Peterson 156) Cooper pairing would be very difficult under these conditions (although this doesn't rule out other pairing mechanisms, certainly)(Ford 73). Physicists needed either to modify the BCS theory, or come up with a completely new theory to explain them. As the critical temperatures continued to rise, from 35 K to 92 K well above liquid nitrogen temperatures of 77 K to finally stand at 133 K in a compound of Hg-Ba-Ca-Cu-O for a compound at normal atmospheric pressure (Ford 68), it became clearer that at least modifications were needed.  Top

First, it has been found that most high-temperature superconductors, when their chemical structure is ever so slightly altered, are antiferromagnetic at low temperatures (although in this state they are not superconducting). The compound La₂CuO₄, which is the basis for La-Ba-Cu-O and other superconducting structures, is antiferromagnetic, as are most of the other base compounds. Superconductivity is achieved, for instance, by doping the compound with barium and allowing it to replace some, but not all, of the lanthanum. The fact that the copper ions don't have full electron shells allows them to display a magnetic moment, and somehow, the rest of the compound lines up the spins of the electrons so that each one points the opposite direction of its neighbor.(This idea is based on the essentially two dimensional nature of the copper sheets, which is where the superconducting actually occurs.) With the spins lined up thus, there is no net magnetic moment. Physicists have been attempting to model how such an ordered spin-pairing could occur, so to better understand the atomic structure of these (almost) superconducting compounds, but they have not been entirely successful. "Sadly, electrons being electrons," as Nature author John Maddox laments, "the problem is not classical but quantal," and thus not quite so easy to solve. (485)

Another interesting feature to note is that most high-Tc ceramic superconductors that were discovered involve compounds of the rare-earth elements yttrium, lanthanum, neodymium, and erbium, among others. Even gadolinium worked, which was surprising to the scientists who made the discovery because gadolinium is strongly magnetic, and the presence of such elements was previously thought to always destroy superconductivity. The low temperature superconductors were, as far as I’ve discovered, all compounds of relatively non-magnetic elements such as aluminum, lead, or nitrogen. (Ford 67, 68)

The amount of oxygen present seems to make a huge difference to the critical temperature of high-Tc superconductors. A chart presented in Ford's article (Figure 1) depicts the transition temperatures for varying oxygen concentrations in the compound YBa₂Cu₃O_7-x (where x is the variable for oxygen content), a black, orthorhombic material. It clearly shows the rise in critical temperature as the oxygen content rises. Although YBa₂Cu₃O_7-x (often abbreviated YBCO) is the compound most often studied, this behavior, to all indications, holds true for the rest of the high-temperature superconductors as well. (Ford 69, 72)

One thing which has been discovered with certainty is that the superconducting layer of superconducting compounds is a very thin CuO₂ layer. This is not to say that a layer of CuO₂ will superconduct on its own �Ethe rest of the structure is also necessary, for it operates as a charge reservoir and allows the establishment of electron pairing. However, these CuO₂ layers are essentially 2-dimensional (in the direction of current flow), and it has been recognized that this factor is essential to the understanding of superconductivity. (Ford 71)

It has been demonstrated that magnetic flux quantization does occur in high-temperature superconductors, and that this quantization occurs in integer values of h/2e. This experiment, which has since been duplicated, indicates that though the pairs may or may not be Cooper pairs, there are indeed paired electrons at work, at least in the YCCO superconductors. From this point, the disagreement over pairing mechanisms arises. One camp argues that Cooper pairs essentially still exist, in essentially the same form, while the other argues that a new pair mechanism is needed to explain these interactions, because Cooper pair interactions as they exist now are too weak to form at such high temperatures. This is essentially where the debate now stands. All the structural clues pretty much indicate some kind of electron pairing what scientists cannot agree on is the nature of the mechanism.   Top

The other kind of symmetry commonly invoked is called d-wave symmetry, and essentially states that the electrons can only move along 45° diagonals to the plane (Figure 2). This would allow the two electrons of the pair to be further away from each other, weakening the repulsion between the two electrons because their linear distance from each other has increased, but allowing them to remain paired. (Kirtley 70)

Because of the distinct natures of these two symmetries, scientists have spent the last several years attempting to determine which one exists in high-Tc superconductors. While no theory has produced a truly distinct symmetry, the elimination of s-wave symmetry, for example, would eliminate the theories which called for that, and the same with eliminating d-wave symmetry possibilities. Narrowing the field would allow proposals to be tested in a more focused manner. (Kirtley 70)

There are several testable properties of d-wave symmetry. The first among them is that Cooper pairs would be more weakly bound to each other in some directions than in others, relative to the atomic matrix, and this would allow for the possibility of unpaired electrons moving along these paths. However, although unpaired electrons were found at low temperatures, the tests conducted on this property were somewhat ambiguous and did not eliminate the possibility of other symmetry states, including, unfortunately, modified s-wave symmetries. (Kirtley 70)

Another method was to look for an angular variation in pairing strengths. This was found to exist, which again would seem to indicate d-waves, but unfortunately, the probability distribution for d-waves includes 4 lobes (see Figure 3), which alternate in sign from positive to negative, and so the data did not make it clear that what was being detected was in fact d-wave symmetry. (Kirtley)

In response to this difficulty, a most intriguing (in my opinion) experiment was carried out by John Kirtley and Chang Tseui of the IBM research labs. Although superconductors expel magnetic fields from their interiors (the Meissner effect), this same property means that superconductors shaped into rings can actually trap magnetic fields inside of the spaces they enclose. The fields, Kirtley explains, "are trapped in discrete bundles, known as flux quanta." We have in fact discussed this property before, as a proof for pairing mechanisms. The total magnetic flux of a quanta is equal to h/2e, as previously stated. (71)

Rings of s-wave superconductors, like mercury or lead, always enclose integer multiples of flux quanta. However, d-wave symmetrical materials can trap half-integer multiples of the flux quanta, and it turns out that this data can be used to determine whether, and where, the lobes alternate in signs. Although the existence of such half-integer quanta was proposed as early as the late 1970s, even before the discovery of high-Tc superconductors, they were not found experimentally until 1993, as a side-effect in an experiment not really designed to look for them. Kirtley's group, according to his article in Scientific American, made the first direct experimental observations and images of half-integer quanta. (71)

Their experiment utilized a quantum-tunneling effect called the Josephson effect. Essentially, when rings of a conducting material (including superconductors) are interupted by thin layers of an insulating material (known as Josephson junctions) electrons will tunnel through them to reach the other side but only if the conducting materials on the two sides of the junction are out of phase with each other. In other words, this tunneling only occurs if the two parts of the ring have opposite signs. By growing YBCO rings with three segments on a substrate and offsetting different sections by 30 degrees (creating Josephson junctions), Kirtley and his team were able to demonstrate that half-integer flux quanta did exist in the rings and in fact, these were all that they found. They found no integer values at all. Control rings with an even number of junctions showed no quanta the sign changed an even number of times and the result is a cancellation. Repeating their experiments with varying setup geometries and other materials demonstrated that the results did indeed indicate d-wave symmetry and not, for instance, some result of the specific details of any particular material or geometry. (Kirtley 72)

Other experimenters at the University of Illinois, the Swiss Federal Institute of Technology, and the University of Maryland have also demonstrated identical results. Kirtley himself seems to have no doubts that high-Tc superconductors demonstrate d-wave symmetry, despite experiments which have indicated s-waves. He notes, however, that this "might be explainable because, under certain circumstances, a cuprate may combine both types of symmetries." (72, 73)

Unfortunately, practically every other theory proposed involves d-wave symmetries. Kirtley also notes that due to varying experimental findings with other superconducting substances that he didn't test, it might be found that not all high-Tc superconductors operate on the same principles (73). This would be discouraging to scientists, who generally like to design their theories to cover all similar physical phenomenon. Top

Although most of the articles I read made no mention of whether they were working with Type I or Type II superconductors, there are in fact two types, as I mentioned before. High-Tc superconductors are all Type II superconductors that is, they display the Meissner effect below a certain critical value, but display superconductivity up to a higher critical temperature (Khurana 17). There are also metallic Type II superconductors, for example NbTi and Nb₃Sn, discovered in the 1960s (Ford 75). The effects of this difference are somewhat interesting, and deserve treatment, particularly since it is because of these that some of the applications of Type II superconductors are possible.

It would logically make sense that if there is no resistance in a superconductor, any current placed within a ring of superconducting material could flow forever. This is actually not so for Type II superconductors. Because Type II superconductors do not completely expel magnetic flux from their interiors, the superconductivity of a Type II superconductor can actually be turned on and off by the introduction or removal of a magnetic field of sufficient strength. The creation of magnetic flux lines within the superconductor creates resistance and destroys the superconductivity (Khurana 18).

"Flux creep" is the phenomenon which causes the resistance. There is an electromagnetic force mentioned in Khurana's article called the "Lorentz" force, which, upon consultation with my physics book, I was unable to locate. However, there is a very simple (and unnamed) phenomenon which we had already discussed in class the fact that a current-carrying wire creates a magnetic field which tends to push the electrons to the side. In class, this was the explanation for the 'jumping�Eof the wires. Here, I believe, the same principle can be applied. Flux creep, it is explained, is the tendency of flux lines to move sideways in the wire, which draws energy away from the electrical current. This only occurs in materials where the flux lattice movement is not restricted by the presence of material impurities or defects that would disallow motion. (Khurana 18)

This flux creep in metallic Type II superconductors is very small �Eit turns out that the decay constant for the current in such superconductors is "longer than the age of the Universe." This allows them to be used to generate large magnetic fields, the applications of which will be discussed in the next section. However, Type II ceramic superconductors generate much larger flux creep values. However, it should also be noted that the lower critical temperature (the one that decides the Meissner effect) is essentially proportional to the critical superconducting temperatures themselves, and so ceramic Type II superconductors have a much higher threshold than do metallic Type II superconductors. (Flux creep can actually be detected by scanning electron microscopes, and its existence, unlike so many other features of high-Tc superconductors, is, to my relief, not in question) Figure 4 shows flux creep at a very low temperature of two different superconductors. The Bi-Sr-Cu-O is near its lattice-melting point, and so displays a large flux creep. (Khurana 18, 19)  Top

MRIs were the first application to be widely investigated, and it is the only application which is in widespead use (there aren't many people who need particle accelerators, and maglev trains are still in the developmental stages). Originally, permanent ferromagnets were used to generate magnetic fields (which allow doctors to non-invasively investigate activity in different parts of the body, most notably the brain). However, it was soon found that Type II superconductors would produce much larger field strengths, on the order of 1T and provided for more uniformity in the field, both of which increased the usefulness and sensitivity of these imaging techniques. The first MRI superconductors were installed in 1979, and the practice has spread world-wide since. (Ford 76)

Particle accelerators use Type II superconductors for very similar reasons they too need the large, stable magnetic fields that Type IIs are capable of generating. Larger magnetic fields meant that the particle's circular path could be kept smaller for higher velocities (since, as we also demonstrated in class, the radius of the particle's circular path in a magnetic field was proportional to the strength of the field). Also, since both the magnets and the bubble chambers used to track particles that the scientists created in collisions necessitated cryogenic temperatures, as well, the two dovetailed nicely. In fact, the energy saved by using superconductors to generate the magnetic fields tends to offset the expense of cooling them. (Ford 76)

Magnetic levitation trains, commonly abbreviated as MAGLEV or, more recently, simply maglev trains, are probably the application which has caught the popular imagination the most. These trains operate on the levitation effects of a strong magnet moving over an ordinary metal track (Ford 77). In an ordinary train, the wheels of course rest on the track, causing a lot of friction due to the great weight of the vehicle. This friction, and the energy costs to overcome the friction and maintain speed, have effectively restricted the speed of these conventional vehicles to under 300 km/hr, or 180 mph. This speed, at the time of Ford's article's publication in 1996, was being approached by the Train à Grande Vitesse (77), otherwise known asthe TGV, or, in English, simply "High-Speed Train." According to Ford, speeds in excess of 500 km/hr (or 300 mph), are envisioned for maglev trains (77).

A survey of information available on the website of the Railway Technical Research Institute (RTRI) in Japan indicates the many factors involved in producing a viable maglev train �Efar more than simply managing to levitate a train on a track. This has already been accomplished, and experimental trains exist in several countries, most notably Japan and Germany. However, there are many more technologies involved in manufacturing such a train, not the least of which is figuring out both braking systems and magnetic shielding of the vehicle itself. In spite of this, RTRI now has several test vehicles running. These include full-size passenger cars (Figure 5), as well as smaller models designed for preliminary testing of braking systems and aerodynamics.

In the schematic of the levitation apparatus (Figure 6) used in a previous test train, which is essentially identical to that used in the mlx01 shown above, the role and location of the superconductors can be seen clearly. The yellow frame, called a bogie, makes up the bottom of the train itself, while the magnets connect to the sides and generate a field in the metal track, which then levitates the train. The superconductors currently in use require cooling to temperatures below that of liquid nitrogen, and so the use of liquid helium is necessary. Using newer superconductors with higher transition temperatures could decrease the energy costs of the system.

One of the drawbacks to the use of high-Tc superconductors has been the inability of scientists to generate large current densities (Jc) in them. According to Ford, most applications which require superconducting magnets require a Jc of 10⁵-10⁶ A/cm² (77). Inital Jc values at 77 K hovered around 10³ A/cm² (Ford 77). However, in a report published by dr. Fujimoto of the RTRI, tests conducted on YBCO compounds were recorded to have a sufficient Jc to produce a 1 T field. Although their samples only generated fields of approximately 0.2 T, Dr. Fujimoto notes that this was for a very small sample of the superconductor. A larger sample, he noted, produced a field of 0.7 T at 77 K. (Fujimoto)

The ISTEC (International Superconductivity Technology Center) has demonstrated the use of an interesting combination of permanent magnets and superconducting magnets, as well, which can yield stronger fields and larger gap separations than superconductors, particularly low Jc ones, alone. (For an entertaining view of a levitating sumo wrestler, access the ISTEC news page).

If it becomes possible, as it seems it soon will, to use superconducting systems that operate above 77 K (i.e., use high-Tc superconductors) much money will be saved in energy costs for systems that already require superconducting magnets or magnetic fields.

However, there is yet another possibility for high-Tc superconductors, although this is still in the future. The use of wires made of superconducting material could greatly decrease home energy costs in the United States and around the world. Since the power dissipation grows in proportion to the current (P=IR²) in normal wires, wires carrying large currents dissipate energy very quickly. The resistance in a wire is also proportional to its length, meaning that the farther away from a power plant a wire has to be laid, the more energy is lost in that wire, even with a relatively small current. If we were able to use superconducting wires, we could greatly cut this energy loss (and consequently cut how much power we have to produce, thereby cutting costs).

This application too is mentioned in RTRI's files. Unfortunately, for it to become practical for wide-spread use, we would have to develop wires that would operate at sufficiently high temperatures to not require cooling. The highest temperature any superconductor has been proven to function at, as of 1996, at least, was 133 K, which is still about -140 degrees Celsius. This is balmy by galactic standards, perhaps, but positively frigid as far as the Earth is concerned. Reports of superconductivity at 240 and 250 K have abounded, but as far as I was able to find, none of these has been produced in large enough samples to be rigorously tested (Alper 1816, Garwin 101). And even the highest of these temperatures would still be some 20 degrees below zero Celsius. For the foreseeable future, widespread use of superconducting wires is not practical.Top
 
 

The main stumbling block to the advancement of the critical superconducting temperature to closer to room temperature is the fact that we do not understand what creates high-Tc superconductivity, and therefore, we cannot predict what materials might show superconducting properties. We essentially take a hit-or-miss approach to the problem, guided by trends that seem to have developed from previous superconductors such as antiferromagnetism or using rare-earth elements and copper-oxygen compounds. An explanatory theory, even incomplete, would give scientists as much better chance at predicting what materials may produce superconductive properties. Then, perhaps, the full effect of resistance-less current flow could be felt throughout our society.