A theory advanced by a Cornell theoretical physicist to link two "broken symmetries" in a high-temperature superconductor has been verified by experiment, bringing scientists a step closer to understanding and perhaps improving superconducting materials.

"Such agreement between theory and experiment is rare since high--temperature superconductivity in cuprates has evaded scientists' understanding for over two decades," said Eun-Ah Kim, assistant professor of physics. "Many models have been proposed, but because this one has been verified by experiment it gives us a jumping-off place for further work."

The results are reported in the July 22 issue of the journal Science with Kim as senior author. The work is a followup to the researchers' previous discovery of a broken symmetry in cuprate bonds reported in the July 15, 2010, issue of Nature.

Under certain conditions, observations with a highly sensitive scanning tunneling microscope (STM) show an anomaly in the distribution of energy levels of the electrons bonding copper and oxygen atoms in a cuprate crystal. There also may be interruptions in the orderly wavelike distribution of those energy levels across the entire crystal. Kim proposed an equation to link the two phenomena.

Simulations based on Kim's theory agree closely with STM observations of a cuprate superconductor containing bismuth, strontium and calcium by co-author J. C. Séamus Davis, the James Gilbert White Distinguished Professor in the Physical Sciences at Cornell. "The notion of symmetry can offer a powerful organizing principle for understanding in physics, if you know which symmetries to focus on," Kim said. "Building on our previous work, we zoomed into two particular broken symmetries."

Superconductivity, where a current flows with zero resistance, was first discovered in metals cooled close to absolute zero (-273 degrees Celsius). Cuprates, made up of copper oxide layers alternating with layers of other "dopant" elements, superconduct at temperatures as "high" as 150 degrees above absolute zero.

An STM uses a probe so tiny that its tip is a single atom, scanned across a surface in steps smaller than the width of an atom. By measuring the current flow between the tip and a surface, Davis can identify the "energy states" of electrons under the probe, which can be thought of as the amount of energy needed to pull an electron loose from its atom. A characteristic of high-temperature superconductors is that certain energy states are missing, and it's believed the missing electrons have gone to form so-called "Cooper pairs" that can move without resistance.

At temperatures above the superconducting transition temperature, cuprates still show this "energy gap," but no longer superconduct. In some materials this "pseudogap" is found all the way up to room temperature, so understanding how it works could show how to design new materials that would superconduct at higher temperatures.

STM images show that in the pseudogap condition the number of electron states varies in a wavelike pattern across a cuprate crystal, so a graph of them looks like ridges in corduroy. But here and there the symmetry of this pattern is broken by what Kim calls singularities, where, for example, one stripe splits into two. Mathematically, these are points where the number of electron states winds up to a peak like a little whirlpool.

More recently, the team found that in the checkerboard arrangement of copper and oxygen in a cuprate, the density of electron energy states between the copper and oxygen atoms is different looking "north and south" than "east and west" -- how much different varies from place to place across the crystal. Kim's theory now predicts that this variation is coupled to the singularities. Singularities should occur at places where the north-south/east-west difference equals the average of such differences across the entire crystal, and STM measurements agree with the prediction. "We have applied this to many sets of data going back almost a decade," Kim said.

The next step, she said, is to see how these locations relate to the arrangement of doping atoms in the crystal layers between copper oxide sheets. That alone may not give us room-temperature superconductors, but it could reveal more about how the pseudogap works.

"Is the pseudogap a preparation for superconductivity or is it inhibiting?" Kim asked. "This development allows us to quantify the degree of broken symmetry and may help answer the question."

The research was supported in part by the National Science Foundation and the U.S. Department of Energy.