Path of electrons in the Tahir-Kheli-Goddard model of high-temperature superconductors. The red arrow indicates the percolating pathway through the plaquettes. Image: Caltech/Tahir-Kheli/Goddard |
It has been 25 years since scientists discovered the first high-temperature
superconductors—copper oxides, or cuprates, that conduct electricity without a shred
of resistance at temperatures much higher than other superconducting metals.
Yet no one has managed to explain why these cuprates are able to superconduct
at all. Now, two Caltech chemists have developed a hypothesis to explain the
strange behavior of these materials, while also pointing the way to a method
for making even higher-temperature superconductors.
Superconductors are invaluable for applications such as MRI machines
because they conduct electricity perfectly, without losing any energy to heat—a
necessary capability for creating large magnetic fields. The problem is that
most superconductors can only function at extremely low temperatures, making
them impractical for most applications because of the expense involved in
cooling them.
A value known as the maximum Tc indicates the highest
temperature at which a material can superconduct. The superconductor used in
MRI—the metal alloy niobium tin—has a maximum Tc of -248 C. Cooling
this material to such a frigid temperature requires liquid helium, a scarce and
extremely expensive commodity.
But the cuprates are different. They still operate well below freezing (the
highest of the high-temperature superconductors, a cuprate created in 1993, has
a maximum Tc of about -135 C), but some can be cooled using liquid
nitrogen. This makes them much more practical, since liquid nitrogen is
plentiful and its cost is about a hundredth that of liquid helium.
The ultimate goal, however, is the creation of superconductors that could
operate near room temperature. These could improve cell-phone tower signaling
and the robustness of the electrical grid, and could one day enable the
operation of levitating trains at dramatically reduced fuel costs.
“But to take superconductors to the next level, we need to understand how
the known high-temperature superconductors work,” says William Goddard
III, the Charles and Mary Ferkel Professor of Chemistry, Materials Science, and
Applied Physics at Caltech. “After the publication of more than 100,000
refereed papers on the topic, there is still no acceptable explanation, and
indeed, there has been no increase in Tc for the last 18
years.”
All superconducting cuprates start as magnetic insulators and are
transformed into superconductors through “doping,” a process that
involves removing electrons from the parent compound, either by substituting
certain atoms for others or by adding or removing oxygen atoms. Still, no one
knows what it is about doping that makes these cuprates superconduct.
Over the last four years, Goddard has published three papers with Jamil
Tahir-Kheli, a senior staff scientist at Caltech, building a hypothesis that
explains what makes cuprates superconduct. They have been working with a
cuprate in which strontium (Sr) atoms are the “dopant atoms,” replacing
lanthanum (La) atoms. Based on modern quantum-mechanical calculations, Goddard
and Tahir-Kheli found that each dopant atom creates a four-center hole on the
copper atoms surrounding the strontium, a unit they refer to as a
“plaquette.” Electrons within the plaquettes form tiny pieces of
metal, while those outside the plaquettes are magnetic. This result was
completely contrary to the assumptions made by most other scientists about what
happens when dopant atoms are added. The problem was, the researchers still did
not know how the holes in the plaquettes led to superconductivity.
It took Goddard and Tahir-Kheli five years to figure that out. Their
hypothesis is that when enough dopant atoms are added, the plaquettes are able
to create a percolating pathway that allows electrons to flow all the way
through the material. The magnetic electrons outside the plaquettes can
interact with the electrons traveling through the plaquette pathway, and “it
is this interaction that leads to the electron pairing—the slight attraction
between electrons—that in turn results in superconductivity,” Tahir-Kheli
says.
The researchers’ latest paper, published earlier this year in the Journal of Physical Chemistry Letters, takes the hypothesis a step further by accounting for a mysterious phase
seen in cuprate superconductors called the pseudogap. In all superconductors,
there is a superconducting energy gap, which is the amount of energy required
to excite an electron from the superconducting state into a higher energy level
not associated with superconductivity. This energy gap vanishes at temperatures
above which a material no longer superconducts—in other words, above Tc.
But in cuprate superconductors, there is a huge energy gap that persists at
temperatures far higher than Tc. This is the pseudogap.
Among scientists, there are two camps on the pseudogap issue. One says that
the pseudogap is connected somehow to superconductivity. The other insists that
it is not connected, and in fact may be a phase that is competing with
superconductivity. Goddard and Tahir-Kheli’s theory lands them in this latter
camp. “We believe that the pseudogap is decreasing the material’s
superconductivity,” Tahir-Kheli says. “And, once again, its origin is
related to the location of the plaquettes.”
Goddard and Tahir-Kheli explain the pseudogap by pointing to plaquettes
that do not contribute to superconductivity. These plaquettes are isolated;
they do not have any other plaquettes directly next to them. The researchers
found that there are two distinct quantum states with equal energy within these
isolated plaquettes. These two states can interact with nearby isolated
plaquettes, at which point the two distinct quantum states become unequal in
energy. That difference in energy is the pseudogap. Therefore, to determine the
size of the pseudogap, all you need to do is count the number of isolated
plaquettes and determine how far away they are from one another.
“The electrons involved in the pseudogap are wasted electrons because
they do not contribute to superconductivity,” Goddard says. “What is
important about them is knowing that, since the pseudogap comes from isolated
plaquettes, if we were to control dopant locations to eliminate isolated
plaquettes, we should be able to increase the superconducting
temperature.”
Goddard and Tahir-Kheli predict that by carefully managing the placement of
dopant atoms, it might be possible to make materials that superconduct at
temperatures as high as -73 C. They note that such an improvement after 18
years of stagnation would mark a significant step toward the creation of truly
high-temperature superconductors with practical implications for the energy and
health sectors.
