``Superconductivity is perhaps the most remarkable physical property in the universe,'' says David Pines, UIUC Center for Advanced Study Professor of physics and electrical and computer engineering, who has been seeking to understand superconductivity for nearly 40 years. Pines' research in physics ranges from microscopic processes to neutron stars.
``What makes superconductors so fascinating is their ability to carry electrical current without resistance and to shield out external magnetic fields,'' he adds.
Discovered in 1911, little progress was made in developing a fundamental theory of their behavior until the 1957 publication of the microscopic theory, or BCS theory, by John Bardeen, Leon N. Cooper, and J. Robert Schrieffer, for which they were awarded the Nobel Prize in Physics in 1972. The BCS theory describes superconductivity in low-temperature metals--such as mercury and lead--and is based on an attractive interaction between electrons that results from their coupling to phonons.
Phonons are quantized modes of atomic vibration that propagate throughout the lattice of a solid. In low-temperature superconductors, quasiparticles (electrons plus their associated screening clouds) disturb the phonons and create a force that overcomes the electrons' repulsive charges. The electrons then form a quantum state made up of Cooper pairs, which cannot scatter off the phonons, thereby eliminating resistance.
Until recently, essentially all superconductors were stable only at exceedingly low temperatures (typically 15 Kelvin, or -258¡ Celsius). Any devices that incorporated them had to be cooled with liquid helium (4.2K), which costs $10 per gallon, and had to be handled by Ph.D.-level technicians. Factors like these have made using these low-temperature superconductors very expensive for commercial applications.
Despite these difficulties, practical uses have resulted, including magnets, such as those in magnetic resonance imaging devices, and SQUIDs (Superconducting Quantum Interference Devices), which are capable of detecting minute magnetic fields.
A clear indication indication of the importance attached to the discovery of these new superconducting materials is that MŸuller and Bednorz were awarded the Nobel Prize [in Physics] within a year of making it--about the fastest turnaround I have seen, Pines says.
With liquid nitrogen 50 times cheaper than helium and thus the promise of commercial viability for the new materials, Pines says that a scramble--involving venture capitalists as well as scientists and engineers--ensued to find new high-temperature superconductors and the reason why they superconduct at such high temperatures.
Condensed matter physicists were particularly caught up in the race. Pines cites a special session of the 1987 American Physical Society meeting--the ``Woodstock of physics,'' it has been called-- for which 4,000 people showed up; that was 2,000 more than the hall could hold!
``Despite the intensive efforts of the theoretical physics community and some 5,000 papers later,'' Pines says, ``there is still no clear consensus on the answers to three fundamental questions about the new superconductors.'' He considers these to be: What is the nature of the normal state? What is the character of the superconducting state? What is the physical origin of their superconductivity?
``What I learned from Bardeen is a `bottom-up' approach to scientific research,'' Pines says. ``You have to first follow the experiment closely, especially when dealing with a major unsolved problem. Second, you should try to keep as open a mind as possible, looking at several possible avenues before fixing upon one when youÕre close to finding the answer.''
Taking Bardeen's philosophy to heart when structuring his research program on high-temperature superconductivity, Pines began with evidence from nuclear magnetic resonance (NMR) experiments carried out by Physicist Charles SlichterÕs UIUC research team.
``These show that the magnetic behavior of the new superconductors is quite bizarre,'' Pines says, so much so that he decided that the magnetic interaction between the electrons in these systems must be playing a key role.
``The basic cause of the magnetic interaction is associated with the fact that electrons have a spin [either up or down] and therefore are capable of interacting magnetically through their spins,'' Pines says. ``In . . . high-temperature superconductors, this magnetic interaction between the electrons can be very strong, changing their normal state behavior and causing the superconducting transition.
``It gives rise not to the usual kind of superconductivity . . . , in which the fundamental interaction is attractive,'' he continues. ``But rather this spin-fluctuation-induced interaction is repulsive for the usual BCS pairs but becomes attractive when one looks at quite subtle effects associated with the relative angular momentum of the pairs of electrons involved.''
``It is enormously important to start out with the right model Hamiltonian for the low-energy properties and then to solve accurately the equations that describe the superconducting transition and the normal state properties, taking into account completely the structure of the magnetic interaction in momentum and frequency space,'' he says. ``You can only do this in a reasonable period of time with a supercomputer. . . .
``If you get an approximate solution, you find that you get completely the wrong answer,'' Pines adds. ``This is one reason why people had not pursued this approach--they couldn't get reasonable quantitative results by following the usual path, making the approximations that were valid for ordinary superconductors.''
Even on a supercomputer, Pines says that carrying out the solution of the Eliashberg equations, which describe the strong coupling effects associated with the spin fluctuations, to the needed degree of accuracy requires a state-of-the-art approach. Philippe Monthoux, then a graduate student in physics at UIUC (and now a postdoc at the Institute for Theoretical Physics, University of California at Santa Barbara), recognized that Fast Fourier Transforms (FFT) would enable accurate solution on NCSA's CRAY Y-MP system. He carried out the calculations in the spring and summer of 1992.
Monthoux says the problem is two-dimensional, with two momentum directions and one ``imaginary'' time dimension. Momenta are described by a 64 x 64 lattice that can have anywhere from 100 to 640 frequencies. The frequencies depend on the temperature, with their number increasing as the system's temperature lowers to the superconducting transition.
According to Monthoux, modeling these frequencies in particular pushes the Cray system's memory limits, with 16 Mwords consumed for most of the runs and 32 Mwords at 640 frequencies. These calculations took in all approximately 150 hours of Cray time.
Regarding its normal state, they discovered that the compound is a quite new state of matter, which they call ``a nearly antiferromagnetic Fermi liquid.'' ``These systems are failed antiferromagnets, in which neighboring spins almost completely line up antiferro-magnetically,'' Pines explains.
He also points out that the location of the spin fluctuations plays an essential role in the high-temperature superconductors. ``The magnetic interaction between the quasiparticles is particularly strong at just those regions in momentum space where it can be effective in bringing about superconductivity.''
From their calculations, it became clear why the superconducting transition for YBa2Cu3O7 occurs at 90K.
The most critical component of the theory concerns the nature of the pairing state. Pines says the theory Òmakes a major prediction about the nature of the pairing state that describes superconductivity. The relative angular momentum must correspond to d-wave pairing, in which the energy gap for quasiparticle excitations in the superconducting state vanishes along selected directions in momentum space.
``[The] pairing state . . . can be checked experimentally directly to see whether it has any chance of being right,'' he continues. ``If the pairing state is anything other than [that] which our theory predicts, the theory is wrong.''
The d-wave pairing differs markedly from the s-wave pairing found in low-temperature superconductors, for which the corresponding energy gap is finite and almost isotropic, Pines says.
During the past few months, the pairing state of the Monthoux/Pines theory has been confirmed by three separate experimental groups. A team led by Walter Hardy, University of British Columbia, has used microwave experiments to investigate the superconducting state, while another team led by Z.-X. Shen, Stanford University, has used angle-resolved photoemissions as a probe.
Newer efforts by Slichter's group at UIUC have again involved NMR, from which Monthoux and Pines first developed much of the spin fluctuation theory. ``The results of the NMR experiments were particularly bizarre and unexpected, yet d-wave pairing provides a quantitative explanation.''
Monthoux adds that he has exhausted the Fast Fourier Transform (FFT). ``We're going to look at a more elaborate model in which the equations are not simple convolutions,'' he explains. ``Then the FFT is of no real use; Iwill have to use finite elements.'' Such work involves very large matrices, which can be efficiently handled on a parallel computer. For these more complex studies, Monthoux will explore using Thinking Machines' CM-5 at NCSA.
While YBa2Cu3O7 is the best characterized compound, Monthoux and Pines are beginning to look at other compounds and other families. They recently applied for additional CRAY Y-MP time to study YBa2Cu3O6.63, a ``reduced oxygen'' compound.
Over time, high-temperature SQUIDs--``if you are clever enough,'' Pines interjects--could measure tiny magnetic waves from the brain that reflect human thought in a field called neuromagnetism. ``This is long-term but not science fiction.''
Perhaps the ultimate superconductor would lose its electrical resistance at room-temperature (approximately 300K). Then, Pines jokes, people could have them in their homes.
He recalls that in the first flush of enthusiasm following MuŸller and Bednorz's discovery, researchers were optimistic about reaching much higher temperatures. ``It is certainly not impossible,'' he says, ``but you'll have to make a material different from anything being made now.''
More realistically, by the year 2000 the threshold for superconductivity could easily be 150K, Pines believes. ``Indeed, someone may have already discovered such a material, but they do not have it in a sufficiently stable form.''
NOTE: A videotaped segment of this project is part the NCSA RealTime #6. To order a copy of this videotape refer to Order for Publications, NCSA Software and Multimedia in the NCSA Contacts Directory.
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access / Spring 1993 / NCSA / pubs@ncsa.uiuc.edu