BY DAWN LEVY
For more than half a century, scientists have been trying to understand why electrons behave differently in different materials. In insulators like glass, where electrons lack the energy to overcome high resistance, they sit around lethargically, barely moving. Conductors like metal, in contrast, have low resistance, and electrons zip around without paying much of an energy cost. Electrons jet through superconductors with virtually no resistance or energy loss. In semiconductors, they act as conductors or insulators, depending on the temperature.
And then there are Mott insulators, named after Nobel laureate the late Sir Neville Mott, a class of complex materials -- typically transition metal oxides -- that buck convention and act as strong insulators despite the fact that electronic theory would have predicted them to be conductors. What is more perplexing, if you replace one element with another -- a technique called doping -- you can change a Mott insulator into a high-temperature superconductor.
Electronic alchemy? Not quite. But understanding bizarre aspects of electron behavior eventually may help scientists unlock the secret of high-temperature superconductors and create other novel materials with electronic and magnetic properties of significance for modern technology. And now scientists have a powerful new spectroscopy technique -- inelastic X-ray scattering (IXS) -- that can help them probe fundamental properties of matter. In a June 9 article in the journal Science, a team of Stanford and Bell Laboratories scientists demonstrated the first-ever use of IXS to study the "energy gap" of Mott insulators, materials that have mystified scientists since their discovery in 1937.
The Science paper shows the feasibility of performing a new class of experiments in condensed-matter physics, says Stanford's M. Zahid Hasan, who led the international collaboration with researchers from Stanford, Bell Laboratories of Lucent Technologies, Ames National Laboratory and Tohoku University in Japan. Hasan is a fourth-year graduate student in applied physics and a research associate at the Stanford Synchrotron Radiation Laboratory (SSRL) of the Stanford Linear Accelerator Center (SLAC).
"Understanding the electronic structure of complex matter is a major intellectual challenge," Hasan says. "So far we know a lot about occupied electronic states in matter, but a lot is unknown about unoccupied electronic states. High-energy inelastic X-ray scattering provides a new way to study the unoccupied electronic states of matter. This opens a new frontier of understanding complex quantum electron systems."
Zhi-Xun Shen, an associate professor in the Departments of Physics and Applied Physics and at the SSRL, says the paper also "suggests that improved instrumentation can significantly enhance the science that can be done."
The material the scientists chose to study was a complex electron system that no one really understands: a prototype of a Mott insulator. Lance Miller at Ames National Laboratory, Iowa State University, provided the material for the experiment by growing a crystal containing calcium, copper, oxygen and chloride.
"The Mott problem has continually challenged our ability to construct a truly comprehensive quantum theory of solids," says Shen. "Today our basic concept of solids is based on the band structure concept. But Mott insulators are a class of materials that cannot be predicted by the band structures." Band structures are used to describe physical laws that govern the numbers and magnetic orientations (spins) of electrons that occupy a given electronic orbital.
"Understanding the band structure for a wide class of materials has played a decisive role in advancing our modern understanding of solids in a microscopic way, and this progress is also responsible for the development of the modern semiconductor industry," Shen says.
Band structure predicts that silicon, for instance, would be a semiconductor, and that is the case. What confounds scientists is that band structures predict that Mott insulators would be metals, which are conductors. But in fact they are excellent insulators.
What gives? It turns out Mott insulators feature an energy gap that is important in these materials but is poorly described by the band theory. The energy gap is an important aspect of the physical properties of solids. Metals, for example, have no energy gap, and electrons can zip around unimpeded. Semiconductors have a relatively small energy gap that makes them extremely temperature-sensitive. And a good conventional insulator like diamond has a very large energy gap. The Mott insulator under investigation here has an energy gap that is larger than that of silicon, the prototypical semiconductor, and yet the band structure did not predict a gap.
When a high-energy photon, or X-ray, scatters from a solid, it loses some of its energy to the electrons in the solid. This "extra" energy is what is needed to excite the electrons across the energy gap. This gap becomes apparent when the energy of the scattered X-ray photon is measured.
"The energy gap concept is very important for a solid," Shen says. He points to four chairs in his office -- two empty, one occupied by a visitor and one occupied by him -- to illustrate consequences of the energy gap. If people were electrons and all the chairs were filled, he says, the office would be an insulator, where people/electrons cannot move to another chair. If you want to move to another chair, you have to go up a flight of stairs to find an empty one, and there's an energy cost to do so. You have to have enough energy to make it up the stairs, or cross the energy gap. In a metal, the chairs are not all filled and people/electrons can travel freely. In a semiconductor, some of the chairs are filled but it doesn't take a lot of energy to get to the next level where the empty chairs are, because they're just a few steps up.
"Researchers have tools that tell them what is below the energy gap, but they know very little about what is above the gap," Hasan says. "Above the gap are states that are not occupied by electrons, yet their nature affects the properties of solids. The new technique is allowing scientists, for the first time, to study the electronic state above the energy gap as a function of direction."
This directional dependence reveals important information about the nature of excitations. In general, directional dependence of the energy gap is a critical parameter of solids. For example, silicon and gallium arsenide (another important semiconductor) have different directional dependence of the energy gap, a fact that determines why gallium arsenide is an important material for semiconductor lasers while silicon is not. "Such information could be directly extracted using this technique, for the first time," Hasan says.
IXS experiments let scientists explore new frontier in condensed-matter physics
Although the technique itself is not new and has been applied by others to study certain sets of problems, Hasan got the idea for applying the technique to the study of complex quantum systems while a graduate student of Professor Arthur Bienenstock, then director of the SSRL. When Bienenstock left Stanford for Washington, D.C., in 1997 to become associate director of the Office of Science and Technology Policy, Hasan continued his studies with a new adviser, Shen, a world expert on angle-resolved photoemission. Together they decided to pursue the idea of using IXS to study complex electron systems and developed a collaboration with researcher Eric Isaacs of Lucent Technologies' Bell Laboratories, a world expert on X-ray scattering spectroscopy.
How does the technique work? Researchers employ synchrotron radiation, or high-energy X-rays produced when charged particles speed around accelerator rings at nearly the speed of light. The X-rays have 10,000 times the energy of the visible light emanating from an ordinary light bulb. Their beams are so tightly focused that they are as sharp as a pinhead. Beams of different energies are used to study different materials. Scientists focus a beam of these X-ray photons onto a material and analyze the energy and direction of the scattered photons.
It is technically challenging to achieve ultra-high-resolution X-ray optics at high energies, and analysis of IXS data is complex. Nonetheless, Hasan and his collaborators were able to show that the technique can be used to study insulators, thanks to the efforts of Bell's Isaacs. "The next step would be to study a wider range of insulators and semiconductors, and even metals, but that endeavor would require further development of synchrotron technologies," Hasan says.
Though SLAC's SSRL has a source of synchrotron radiation, it is in the process of being upgraded under the guidance of SSRL Director Keith Hodgson with $90 million from the Department of Energy and the National Institutes of Health. The upgrade will be complete in 2002, and experiments can begin there in 2003. For this reason Hasan's experiment had to be conducted at the National Synchrotron Light Source (NSLS), a facility at Brookhaven National Laboratory in Long Island, N.Y., where Department of Energy staff provided technical expertise and where Bell Laboratories, among others, set up an experimental station in which this experiment was conducted.
Hasan also spent time at the Advanced Photon Source (Argonne National Laboratory, Chicago), Bell Laboratories, Lucent Technologies (Murray Hill, N.J.), European Synchrotron Radiation Facility (Grenoble, France) and Advanced Light Source (Lawrence Berkeley National Laboratory, Berkeley, Calif.) to develop the necessary ideas for this class of experiments. "I had to travel around the world to get this experiment going," Hasan says.
Isaacs of Bell Labs was a key collaborator, providing scientific and technical support in the design, set-up and performance of the experiment. He and researcher Peter Abbamonte helped Hasan learn the details of high-energy scattering. Kenji Tsutsui, Takami Tohyama and Sadamichi Maekawa of Tohoku University in Japan performed a computer simulation of the experiment. The simulation was based on the Hubbard model, which is a classical model used to describe Mott insulators and considers two fundamental characteristics of a complex electron system -- "hopping freedom" of an electron from one site to another and a strong charge repulsion between two electrons. Using such assumptions, scientists attempt to simulate the behavior of electrons with computers. Indeed, the simulation shows many features that are consistent with the experimental data. The results reaffirm the long-held but untested assumption that the Hubbard model accurately describes the key physics of Mott insulators.
Technique eventually may tackle increased complexity in biological systems
Right now the research is "at a pioneering level," says Hasan, and it is hard to tell where it will have future impact. Eventually, he hopes to use the technique to study "the ultimate complex systems" -- biological systems. "The intellectual developments in complex systems indicate that a long-cherished scientific reductionist worldview might be falling apart," he says. "The unsolved problem of 'apparently simple' Mott insulators is just a glimpse of that new frontier. The complexity of biological systems far exceeds the level we can deal with at this moment. Besides an intellectual paradigm shift, you don't know which technological revolution these complex systems would lead to. It is not predictable."
What is predictable is a shift in facility use from physics to biology research. The SSRL's Stanford Positron Electron Accelerating Ring (SPEAR) originally was built for high-energy particle physics experiments and spawned work for which Burton Richter in 1976 and Martin Perl in 1995 won Nobel Prizes. Its use since has evolved to include solid-state and materials-related physics and chemistry research as well as medical, biological and environmental sciences. Basic physics work is now "the minority there," says Shen, who estimates that more than 60 percent of SSRL users are biologists. Hasan thinks an upgraded synchrotron facility will "add a color to the broad spectrum of the Stanford Bio-X program, too."
IXS spectroscopy capabilities are being developed in many high-energy synchrotron facilities around the world, including the European Synchrotron Radiation Facility (Grenoble, France) and SPring8 (Tsukuba, Japan). In the United States, Department of Energy facilities such as Argonne, Brookhaven and Lawrence Berkeley National Laboratories are developing IXS capabilities. "Stanford University has all the resources to take a leading role in advancing this new frontier of complex system research by developing such a facility at SSRL," Hasan says.
The work was supported by funds from
the Department of Energy, Office of Basic Energy through SSRL and
Ames Laboratory; Lucent Technologies' Bell Labs; the Ministry of
Education, Science, Sports and Culture (Japan); Center for
Renewable Energy and Sustainable Technology (CREST); and New Energy
and Industrial Technology Development Organization (NEDO).