The Story of High Temperature Superconductors

Thomas Devereaux
Department of Physics
University of Waterloo
N2L 3G1

Phone: 519-888-4567 x 6901
Fax: 519-746-8115
Email: tpd@lorax.uwaterloo.ca or tpdevereaux@earthlink.com
http://sciborg.uwaterloo.ca/~tpd

It was standing room only as thousands of physicists packed into several ballrooms serving as a single meeting room.  The session was going late into the evening and would continue into the early March morning. Almost all of the world’s experts on superconductivity, including several Nobel laureates, gave short talks on their take on recent events. The usual structure of the conference had been abandoned as the latest news was eagerly conveyed and received that a family of materials was found with superconducting transition temperatures near 100 degrees Kelvin.
That was in 1987 at the American Physical Society (APS) March meeting in New York, which The New York Times called the “Woodstock” of physics. Unfortunately for me, I was still more concerned about Max Yasgur’s version rather than the APS one, but shortly thereafter I was drawn into the burgeoning fray along with many other condensed matter theorists.
It is now 13 years since that Woodstock happened, and you would think that by now we’ve wrapped the whole subject up into a nice well-understood package. But unfortunately, we don’t have high temperature superconductors in our computers and cell phones yet, haven’t solved the energy crisis by having found materials which superconduct at liquid nitrogen temperatures, and haven’t put people (actually much of anything) on Mars. In fact, it may appear to most people that we have not even begun to fulfill the promises that were all over The New York Times and other media outlets in 1987.  This is a simple testament to the fact that the understanding of high temperature superconductivity has been and still is one of the most important and most difficult unsolved problems in physics.
To put the discovery by Bednorz and Müller into perspective, in the 75 years prior to their discovery superconductivity was an interesting field, but if you took a theorist and pinched him or her they would soon admit to you that it pretty much was a story that had already been told. After numerous efforts, the transition temperature was still pitifully cold (around 23 Kelvin) and it was a widely held belief that in fact it would be impossible to increase it much further.
Like many of the achievements that science brings us, most people would say that this one was sheer dumb luck. Bednorz and Müller were on what was thought to be a wild goose chase: using the trial-and-error method of mixing poorly conducting oxides to see whether they could find high temperature superconductivity. Miraculously, they actually went out and found it in 1986 (and of course got a Nobel prize for it). Their results turned the physics community and our perceptions of superconductivity upside down.
The high temperature superconductors (cuprates) consist of copper oxide (CuO2) layers separated by large spacing ions such as barium, bismuth, strontium or yttrium. Most of the stoichiometric parent compounds such as La2CuO4 are antiferromagnetic insulators. However when doped either with other ions off the CuO2 plane (such as Sr), or more oxygen, the materials quickly evolve into high temperature superconductors (see the phase diagram in Figure 3). Empirically, the more toxic they are (containing e.g., mercury or thallium) the higher the transition temperature. Even when made to be non-toxic, these materials are really poor metals— in fact, they are ceramics. They poorly conduct electricity in their normal state and are extremely brittle, presenting problems to bend them into wires and devices. It is counterintuitive to say the least that we should try to use these materials for electric motors or transmission wires rather than coffee cups. However we’ve come to realize that it is generally true that poor metals make the best superconductors while the best metals (gold, platinum, copper) may only be superconducting at extremely low temperatures. But, we don’t have a good reason why. On top of that, with small doping changes, the cuprates simultaneously show magnetic features as well as superconductivity, and everything we had learned before had told us that magnetism hurts superconductivity. Yet in this case, it is now widely believed that the incipient magnetism actually gives rise to high temperature superconductivity. Lastly, even our understanding of what it means to be “normal” has been challenged. These materials have defied a simple description in terms of the canonical theory of metals (Fermi liquid theory) that has been so successful in describing the behavior of most metals. For these reasons, it is not a stretch to call these materials a "new phase of matter".
The challenge to describe this “new phase of matter” has attracted the brightest minds and has resulted in many new and exciting probes to probe the delicate behavior of these materials. 
The Nobel Prize-winning work of Bardeen, Cooper, and Schrieffer (BCS) gave us a thorough framework for understanding superconductivity. In most conventional low temperature superconductors, electrons pair into more or less an isotropic bound state (s- wave) due to the dynamical distortion of the lattice (phonons). The high temperature superconductors dramatically challenged that picture. Efforts at constructing a theory for these new materials quickly broke into two camps: those that thought that the existing BCS theory just need a small “tweak”, and others who believed that an entirely new approach was needed. The former believed that the electrons could be treated as a liquid of more or less weakly interacting particles, and that superconductivity was as conventional as lead. The latter group believed that even our starting point was wrong: the interactions between electrons are so strong that they obliterate the standard Fermi liquid picture (implying that the lattice is irrelevant for superconductivity). This problem was so important and vexing that understanding superconductivity would be impossible without understanding this “new phase” of matter first.
With everyone in agreement that the person to come up with the correct theory will be guaranteed a Nobel Prize, the high stakes meant that tempers often flared and turf battles were raged. This of course was a great time to learn about human psychology as well as physics. It was commonplace to see theorists run around with their special data set, which was the smoking gun that proved their theory. The problem was that there were as many smoking guns as there were theories, and every theory was completely orthogonal to every other theory. It was amusing just to keep track of who was pushing what as theories changed as often as fashion. 
However, we still do have a convergent series approach to the problem. Due largely in part to beautifully devised experiments over the past few years meant to test esoteric quantities such as the phase of the order parameter, it is now widely accepted that the electrons in the cuprates pair in a d-wave orbital wave function and that the pairing is mediated largely by exchange of damped magnons (antiferromagnetic spin waves) rather than phonons. But to a certain extent, that is where the agreement ends.
What is the crux to the problem of high temperature superconductivity? To many it is the answer to the physics of competing instabilities in restricted dimensions. The cuprates possess various instabilities—they show tendencies for spin, charge, and superconducting order that may coexist over portions of the phase diagram. This is suggestive of the influence of one or several underlying quantum critical points (such the Mott transition from metal to insulator) and most of the tendencies for spin, charge, and superconducting order arise from the proximity to the quantum critical point. Unfortunately, there are still very few definitive calculations available to test against experiments.
In fact, developments of a theory have gotten downright philosophical. As of late the debate has evolved into a question of “organizing principle”. The idea is that we still are missing the single organizing principle from which the behavior of the cuprates can be easily explained. Recently, David Pines at the University of Illinois at Urbana-Champaign coined the phrase “Quantum Protectorate” (QP) which taken loosely means that the one organizing principle can describe the qualitative behavior of the system and is only marginally dependent on the actual microscopic details of the material. For example, the Fermi liquid theory can be viewed as a QP in that most metals can be described with a single formalism and the differences between say copper and aluminum are only of minor consequence. Another example is BCS theory itself. The organizing principle is the phase coherent pairing of electrons, and that single principle allows a complete description of the properties of that phase, whether it is lead, aluminum, or tin. For the high temperature superconductors, the organizing principle should in a natural way explain the complex phase diagram of the cuprates, which includes metallic behavior, antiferromagnetic insulator, superconductor, pseudogaps (gaps with no accompanying phase transition), and charge ordering in the form of stripes.
From the technological point of view of course, the existence of a microscopic theory may be completely irrelevant. In spite of the absence of a theory, technological advances have come at a steady pace. One of the most touted promises of cuprates was their use in Maglevs, or magnetically levitated trains. In a recent run on a test track in Japan, a five-car train (with a few passengers) levitated over guide rails reached a sustainable speed of over 550 km/hr. But bigger things are coming and the real benefits may be closer than we think. Recently, American Superconductor (AMSC) reported the development of a 17 km long wire with a average critical current in excess of 16 kA/cm2. Along with AMSC, the US Navy has been developing engines using superconducting magnets that are capable of over 25,000 horsepower to power future Navy ships. Spin-off technology has made possible the use of superconducting quantum interference devices (SQUIDS) for biomagnetic sensors (magnetoencephalography) to complement magnetic resonance imaging to visualize in real time the normal functions and functional disorders (such as schizophrenia) of the brain. But in perhaps the most significant development to date, in Detroit this fall three superconducting cables will be put in place to carry 100 million watts of power in a power utility network. This will be hopefully the first stage of a general plan to replace the US electrical grid with superconducting cables. This certainly conveys comparison to the way that fiber optics revolutionized telecommunications. According to Kurt Yeager, President & CEO of Electric Power Research Institute, “We’ve just completed the first electrical century, ushered in by Thomas Edison. We’re now entering a second electrical century, ushered in by high temperature superconductivity.”
Which brings the story full circle. Recently, at a conference in Houston I was trying to get into a session on the theory of the cuprates, and found that I was at least six people deep from the entrance to the meeting room. So 14 years later, we still have the same excitement for the field and in the field, and are still working away trying to solve one of the more vexing problems in all of physics.

Useless Information

I recently arrived at the University of Waterloo this past September. Prior to that I was an assistant professor of physics at George Washington University, just four blocks from the White House. 
My general field of research concerns the interplay of interactions, disorder, and superconductivity. I’ve chosen to attack the cuprates by working on the theory of transport and optical properties of these materials. My work has focused on making contact to experiments on electronic and phonon Raman scattering, infrared conductivity, scanning tunneling microscope measurements, and the critical currents and behavior of vortices created by magnetic fields in high temperature superconductors. For more information, including more cerebral descriptions of my work as well as sample publications, please visit my web site at http://sciborg.uwaterloo.ca/~tpd.
More useful links:
http://www.amsuper.com
http://superconductors.org
http://www.iitap.iastate.edu/htcu/htcu.html
http://dali.roma1.infn.it/htcs/htcs.html