Superconductivity associated with fractal structure of nanoscale electron lines

A collaborative investigation between the University of Illinois and Purdue University has shed new light on the fundamental physics that govern the pattern formation observed in the superconducting phase.

By applying a new method of analysis involving fractal geometry, Karin Dahmen, an associate professor of physics at Illinois, along with Purdue physics doctoral candidate Benjamin Phillabaum and Purdue physicist Erica Carlson, found that nanoscale electron lines observed on the surface of some high-temperature superconductors actually originate deep within the material.

The group’s findings, published in "Spatial complexity due to bulk electronic nematicity in a superconducting underdoped cuprate," in the June 26, 2012 issue of Nature Communications, may unlock the potential for designing even better high-temperature superconductors in the future.  

“The study of superconductors is one of the most interesting and potentially most useful endeavors of modern physics,” said Dahmen. “Any improvement in our understanding of superconductivity may have huge implications for technical applications down the road. If we fully understand how superconductors can conduct current without any resistance, someday we may be able to build superconducting materials that can do this at room temperature. Our electricity bills would shrink to a minimum when that is possible.” 

Prior to this study, researchers using surface probes had observed the formation of nanoscale lines on the surfaces of high temperature superconductive materials, during the phase just before critical temperatures for superconductivity are reached. It’s been suggested that these lines could explain how high-temperature superconductors are able to superconduct, but until now, physicists could not look below the surface to know whether the nanoscale lines occur throughout the superconducting material.

“The behavior of electrons inside of copper-oxygen based high-temperature superconductors has puzzled researchers since their discovery in 1986,” said Carlson. “By all rights, these ceramic materials have no business conducting electricity at all, but under the right conditions, they do conduct electricity, and they do it perfectly, without losing energy.” 

The investigators began their analysis by comparing data published in various experimental studies. They zeroed in on fingery (or fractal) regions of electron lines apparent across the data. Next, the team used geometry to analyze the patterns of the nanoscale electron lines on the surface of the materials, treating sets of neighboring parallel lines as part of a single cluster.

Said Dahmen, “We decided to make histograms of the sizes of these regions and compare them with predictions from various models. We found they agreed with those from models that also had fingery regions in the bulk of the material—the agreement was striking.”

Carlson explained, “We noticed that the pattern of orientations of the nanoscale lines doesn’t depend on the scale of the image. The pattern looks the same whether we view the entire image, or whether we view smaller and smaller pieces of it—the pattern is fractal.

“Every fractal has its own set of characteristic numbers, as unique as a fingerprint. You might imagine that the characteristic numbers for a fractal which is happening only on the surface would be different from the characteristic numbers for a fractal which really originates from deep inside the material.

“When we studied the characteristic numbers of this fractal, we discovered telltale signs in its fingerprint that indicate this is not just a surface fractal.  Rather, it is coming from deep inside the material. We are seeing a 3-D fractal, which then intersects the surface of the material.” 

This new method of analysis has potential for broad application in investigating other superconducting materials as well.

“You can study the surface properties of materials, and from the statistics of the surface properties draw conclusions about the structure in the bulk of the material,” said Dahmen.  The team plans to look next at pattern formation in other superconductive materials, including a new class of iron-based high temperature superconductors, the colossal magnetoresistance materials known as manganites, and even the “memristor” materials known as vanadium oxides. 

“Memristors are like resistors combined with memory—you can ‘write’ to the memristor, telling it to be high resistance, until you erase that information, at which point the memristor reverts back to its low resistance state,” said Carlson.  “This is only a step towards understanding superconductivity better. Now a lot more work needs to be done to explain this phenomenon,” said Dahmen.

Acknowledgements: B.P. and E.W.C. acknowledge support from Research Corporation for Science Advancement and NSF Grant No. DMR 11-06187. K.A.D. acknowledges support from NSF Grant No. DMR 10-05209 and from the Materials Computation Center [NSF DMR 03-25939 (MCC)]. E.W.C. thanks École Supérieure de Physique et de Chimie Industrielles (ESPCI) for hospitality. The conclusions presented are those of the scientists and not necessarily those of the funding agencies.
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Contact: Karin A. Dahmen, Department of Physics, 217/244-8873.

Writer: Siv Schwink, Department of Physics, 217/552-5671.

If you have any questions about the College of Engineering, or other story ideas, contact Rick Kubetz, editor, Engineering Communications Office, University of Illinois at Urbana-Champaign, 217/244-7716.