Monday, July 21, 2008

High-temperature superconductivity

"Normal" superconductivity is a phenomenon that has been known to physicists since 1911, when it was discovered by Heike Kamerlingh Onnes. The phenomenon involves the essentially total loss of electrical resistance in certain materials – mostly metals and metallic alloys – at temperatures very close to absolute zero (0° K, which is -273.15° C). Most metallic elements, except for ferromagnetic metals and some noble metals like silver and gold, become superconducting at sufficiently low temperatures.

The low temperatures needed for normal superconductivity are now easily maintainable in the laboratory, for instance by immersion in liquid helium, which has a boiling point of 4.22° K. Although such temperatures are routinely achievable, it's not easy or cheap to do so. Nevertheless, even some very large devices, such as the Large Hadron Collider, depend on superconductivity in their operation.

It is quite easy to measure experimentally when superconductivity is occurring, because Ohm's Law states that V=I×R, where V is voltage, I is current, and R is resistance. Consequently, resistance is given by R=V/I. So if there is a current flowing between two points in a material even though the voltage difference is zero, the resistance must be zero.

In most materials, resistance decreases as the temperature decreases. In superconductors, by definition, there is a temperature, called the critical temperature (TC), at which resistance abruptly becomes essentially 0. By that we mean the resistance is too low to measure, and an electric current flowing in a superconducting material does not dissipate any measurable heat. So the current (I) can flow for an indefinitely long period of time, without any loss.

Clearly, superconductivity is an extremely useful property to have in a material. It could, for example, allow transmission of electricity over wires without any loss at all, as opposed to the loss that normally occurs due to generation of heat. Unfortunately, the highest critical temperature known in a "normal" superconducting material is about 39° K. That record was established in 2001 with magnesium diboride (MgB2). Liquid helium isn't needed to keep such a material in a superconducting state. Liquid nitrogen, which is commonly used commercially and has a boiling point of 77.36°K (-195.79° C) suffices, even though it has to be kept cooled to well below its boiling point.

So it was with high hopes that the discovery in 1986 of "high-temperature" superconductors was greeted. One measure of the perceived importance of the discovery is the fact that the discoverers (Karl Müller and Johannes Bednorz) were awarded a Nobel Prize the very next year.

There were strong hopes at the time that eventually materials would be discovered that exhibited high-temperature superconductivity even at room temperatures. This would make possible the economical production of useful things like maglev trains. Although maglev trains have in fact been built that use high-temperature superconductors, the requirement for liquid nitrogen still makes them very expensive to build and maintain.

High-temperature superconductivity was first observed in ceramics based on copper oxide (CuO2). The material also incorporated the elements lanthanum and barium, and had a transition temperature of about 35°K. Just two days ago it was announced that a rather more exotic cuprate material, incorporating tin, lead, indium, barium, and thulium, had the highest TC found so far, about 195° K (-78° C) – that's the sublimation temperature of CO2. (See here.)

Although 195° K is a huge improvement over 35°K, it is still far below "room temperature". This still makes the routine use of high-temperature superconductors in most applications uneconomical, or at best difficult. There's an additional problem in that most high-TC materials are ceramics, so they lack the ductility of metallic materials, which is often required in practical applications like wires and cables. Furthermore, such materials are generally tricky to manufacture at all, and require exotic elements like thulium.

For all the reasons mentioned, more than 20 years after the discovery of high-TC materials, there is a great deal of disappointment and frustration that progress hasn't lived up to the initial high hopes.

One of the main obstacles to progress has been the surprising fact that we do not even have an adequate theory of how high-temperature superconductivity works. We do have a good theory of how "normal" superconductivity works, but that theory, even with tweaks, does not appear to be applicable at temperatures more than about 40° K. Before 1986, the highest TC known was 23° K. So at first it might seem as though 35° K was not that big an advance.

However, in 1986 it was thought that the existing theory did not apply at temperatures more than about 30° K. The fact that in 1986 both theory and experiment did not anticipate a TC of 35°K is what made the discovery so unexpected. The fact we still don't have an adequate theory for most high-TC materials means it isn't possible to figure out theoretically what sorts of materials might have TC exceeding the currently known upper limit.

So let's quickly review the theory of "normal" superconductivity. It's surprisingly simple (which is also why it doesn't extend beyond 40°K). The theory is known as BCS theory, for its developers, John Bardeen, Leon Cooper, and John Schrieffer.

Electrical conductivity at ordinary temperatures is based, of course, on the largely free movement of electrons in a metallic or semi-metallic material. Resistance is simply the result of interactions that transfer energy from the electrons to atoms of the material. Eventually all the energy carried by the electrons is dissipated as heat, and the current (I) goes to 0, unless energy is supplied (say, from a battery).

According to BCS theory, at sufficiently low temperatures two electrons having opposite spins pair up with each other to form "Cooper pairs". Electrons normally repel each other due to the Coulomb force resulting from their electrical charge. But each electron also, because of Coulomb force, distorts the lattice of positively charged ions of the material. This distortion is called a "phonon". In fact, the distortion itself has a vibrational, wavelike nature – like the quantum wavelike behavior of an electron or any other subatomic particle.

A phonon has a net positive charge of nearly the same magnitude as the negative charge of an electron, so this pairing mostly cancels out the electrical charge of the electron-phonon pair. But the cancellation is only approximate, so that each electron-phonon pair has a small net charge, which may be positive or negative. Consequently, electron-phonon pairs can attract other pairs having opposite charge. The Cooper pair is this pairing between electron-phonon pairs.

Cooper pairs form only when the electrons involved have opposite spins. Consequently, a Cooper pair has zero net spin, making it a boson. This is important in BCS theory, since bosons aren't subject to the Pauli exclusion principle. The result is that many Cooper pairs can be simultaneously in the same quantum state.

At a sufficiently low temperature it becomes impossible for Cooper pairs to interact with the lattice of the material. This is because, due to the Heisenberg uncertainty principle, there is a lower limit on the amount of energy (ΔE) that can be exchanged between a Cooper pair and the lattice. If the binding energy within the Cooper pair is less than ΔE, no interaction that disrupts the pair is possible, so the pair represents a stable bound state. It can therefore move completely freely within the lattice, with no resistance at all.

The net result is that the electrons which are paired up within Cooper pairs can move completely freely within the lattice. And since electrons themselves still have a net charge, the effective result is an electrical current that flows with zero resistance. Another way of thinking about this is that a pair of electrons moves through the lattice accompanied by distortions of the lattice, but in such a way that no energy is transferred to the lattice.

If all this legerdemain seems a little suspicious, remember that it's a quantum effect that is possible only at very low temperatures, and that's why the BCS theory does not apply, even with any variations that physicists have been able to conceive, above approximately 40° K.

Materials capable of high-temperature superconductivity are more complex than typical "normal" superconducting materials. The latter include many metallic elements, such as mercury or lead. But the former are ceramics, which are often, but not always, based on copper oxide. In the so-called cuprate superconductors, atoms of additional elements are included between planes consisting of copper oxide. This process is referred to as "doping". It has the effect of inserting either a surplus or a deficit of electrons (called "holes" in the latter case), and it is these electrons and holes that are available for carrying electric charge in the material.

It is thought that these electrons and holes are able to pair up in some way that is analogous to Cooper pairs, and that the resulting pairs are the necessary bosonic charge carriers. But one basic problem in this field is that it has not even been possible to determine experimentally exactly what the hypothetical pairs consist of.

There is a vast theoretical and experimental literature, estimated as upwards of 100,000 published papers, dealing with the field of high-temperature superconductivity. Nevertheless, the development of an adequate theory to explain the effect is still considered to be one of the most important unsolved problems in condensed matter phyaics.

Now there is additional experimental work that claims to have made significant progress:

Room Temperature Superconductivity: One Step Closer To Holy Grail Of Physics (7/9/08)
The researchers have discovered where the charge 'hole' carriers that play a significant role in the superconductivity originate within the electronic structure of copper-oxide superconductors. These findings are particularly important for the next step of deciphering the glue that binds the holes together and determining what enables them to superconduct.

Dr Suchitra E. Sebastian, lead author of the study, commented, "An experimental difficulty in the past has been accessing the underlying microscopics of the system once it begins to superconduct. Superconductivity throws a manner of 'veil' over the system, hiding its inner workings from experimental probes. A major advance has been our use of high magnetic fields, which punch holes through the superconducting shroud, known as vortices - regions where superconductivity is destroyed, through which the underlying electronic structure can be probed.

"We have successfully unearthed for the first time in a high temperature superconductor the location in the electronic structure where 'pockets' of doped hole carriers aggregate. Our experiments have thus made an important advance toward understanding how superconducting pairs form out of these hole pockets."

By determining exactly where the doped holes aggregate in the electronic structure of these superconductors, the researchers have been able to advance understanding in two vital areas:

(1) A direct probe revealing the location and size of pockets of holes is an essential step to determining how these particles stick together to superconduct.

(2) Their experiments have successfully accessed the region betwixt magnetism and superconductivity: when the superconducting veil is partially lifted, their experiments suggest the existence of underlying magnetism which shapes the hole pockets. Interplay between magnetism and superconductivity is therefore indicated - leading to the next question to be addressed.

Do these forms of order compete, with magnetism appearing in the vortex regions where superconductivity is killed, as they suggest? Or do they complement each other by some more intricate mechanism? One possibility they suggest for the coexistence of two very different physical phenomena is that the non-superconducting vortex cores may behave in concert, exhibiting collective magnetism while the rest of the material superconducts.

Further reading:

A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor – original research paper (sub. rqd.)

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Blogger Jifbo said...

Nice Post, helped me understand why superconductors behave as they do!

Keep it up,

1/28/2009 12:47:00 PM  

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