Although high-temperature superconductors are widely used in
technologies such as MRI machines, explaining the unusual properties of these
materials remains an unsolved problem for theoretical physicists. Major
progress in this important field has now been reported by physicists at the University of California,
Santa Cruz, in
a pair of papers published in Physical Review Letters.
The first
paper, by UCSC physicist Sriram Shastry, presents a new theory of
“Extremely Correlated Fermi Liquids.” The second paper
compares calculations based on this theory to experimental data from studies of
high-temperature superconductors using a technique called angle-resolved
photoemission spectroscopy (ARPES). The lead author of this second paper is
Gey-Hong Gweon, assistant professor of physics at UC Santa Cruz, with coauthors
Shastry and Genda Gu of Brookhaven National Laboratory.
“I showed my preliminary calculations to Gweon, who is
an expert in this field, and he was very excited,” says Shastry, a
distinguished professor of physics at UCSC. “He obtained data from lots of
experimental groups, including his own, and we found a remarkably successful
agreement between theory and experiment at a level that has never been achieved
before in this field.”
Shastry’s theory provides a new technique to calculate from
first principles the mathematical functions related to the behavior of
electrons in a high-temperature superconductor. Interactions between electrons,
which behave as almost free particles in normal metals, are a key factor in
superconductivity, and these electron-electron interactions or correlations are
directly encoded in photoemission spectra.
Photoemission spectroscopy is based on the photoelectric
effect, in which a material emits electrons as a result of energy absorbed from
light shining on the surface of the material. ARPES studies, which produce a
spectrum or “line shape” providing clues to the fundamental
properties of the material, have yielded anomalous results for high-temperature
superconductors.
“The unusual ‘fatness’ of the line shapes observed in
electron spectroscopy has been at the center of the mystery of high-temperature
superconductors,” Gweon says. “The anomalously broad and asymmetric
line shape has been taken as a key signature of strong electron-electron
interaction.”
Shastry’s theory of extremely correlated Fermi liquids is an
alternative to the Landau Fermi liquid theory, which is a highly successful
model for the weakly interacting electrons in a normal metal but not for very
strongly correlated systems. The success of Shastry’s calculations indicates
that the anomalous photoemission spectra of high-temperature superconductors
are driven by extreme correlations of electrons. Shastry coined the term
“extreme correlation” to describe systems in which certain
“energy expensive” configurations of electrons are prohibited. This
arises mathematically from sending one of the variables, known as the Hubbard
“U” energy, to infinity.
“That leaves you with a problem that is very hard to
solve,” Shastry says. “I have been studying these problems since
1984, and now I have found a scheme that gives us a road through the impasse.
The spectacular correspondence with the experimental data tells us that we are
on the right track.”
The experimental data come from ARPES studies using two
different sources of light: high-energy light from synchrotron sources and
lower-energy laser sources. In studies of high-temperature superconductors,
these two light sources yield significantly different photoemission spectra for
the same samples, and researchers have been unable to resolve this
inconsistency. But Gweon and Shastry found that these apparently irreconcilable
results can be accounted for by the same theoretical functions, with a simple
change in one parameter.
“We can fit both laser and synchrotron data with
absolute precision, which suggests that the two techniques are consistent with
each other,” Shastry says. “They are telling two different slices of
the same physical result.”
Shastry says he plans to use the new technique to calculate
other experimentally observed phenomena. “There is still a lot of work to
be done,” he says. “We have to look at a variety of other things, and
extend the new scheme to do other calculations. But we have made a breach
through the impasse, and that’s why we are excited.”
