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, Purdue physics doctoral candidate Benjamin Phillabaum, Purdue physicist Erica Carlson, and UI physicist Karin Dahmen have 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 the June 26, 2012 issue of Nature Communications, may unlock the potential for designing even better high-temperature superconductors in the future.
Written by Siv Schwink
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, UI physicist Karin Dahmen, Purdue physics doctoral candidate Benjamin Phillabaum, and Purdue physicist Erica Carlson have found that nanoscale electron lines observed on the surface of some high-temperature superconductors actually originate deep within the material.
“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.
This illustration depicts a scanning tunneling microscope at the surface of a material with fractal clusters (shown in yellow) that actually extend into the bulk. Phillabaum, Carlson and Dahmen introduce a new set of methods for analyzing strongly correlated electronic systems,
exploiting the fractal nature of electronic clusters to enable surface probes to peer deep inside materials. Using these new methods, the team finds that nematic electronic clusters large enough
to support a nematic-based mechanism of high temperature superconductivity
extend throughout the bulk of the material.
“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.
Madeline Stover is a physics doctoral student at the University of Illinois Urbana-Champaign studying atmospheric dynamics applied to forest conservation. She interns as a science writer for Illinois Physics, where she also co-hosts the podcast Emergence along with fellow physics graduate student Mari Cieszynski. When Stover is not doing research or communications, she enjoys hosting her local radio show, singing with her band, and cooking with friends.
Daniel Inafuku graduated from Illinois Physics with a PhD and now works as a science writer. At Illinois, he conducted scientific research in mathematical biology and mathematical physics. In addition to his research interests, Daniel is a science video media creator.
Karmela Padavic-Callaghan, Ph. D. is a science writer and an educator. She teaches college and high school physics and mathematics courses, and her writing has been published in popular science outlets such as WIRED, Scientific American, Physics World, and New Scientist. She earned a Ph. D. in Physics from UIUC in 2019 and currently lives in Brooklyn, NY.
Jamie Hendrickson is a writer and content creator in higher education communications. They earned their M.A. in Russian, East European, and Eurasian Studies from the University of Illinois Urbana-Champaign in 2021. In addition to their communications work, they are a published area studies scholar and Russian-to-English translator.
Garrett R. Williams is an Illinois Physics Ph.D. Candidate and science writer. He has been recognized as the winner of the 2020 APS History of Physics Essay Competition and as a finalist in the 2021 AAAS Science and Human Rights Essay Competition. He was also an invited author in the 2021 #BlackinPhysics Week series published by Physics Today and Physics World.
Karmela Padavic-Callaghan, Ph. D. is a science writer and an educator. She teaches college and high school physics and mathematics courses, and her writing has been published in popular science outlets such as WIRED, Scientific American, Physics World, and New Scientist. She earned a Ph. D. in Physics from UIUC in 2019 and currently lives in Brooklyn, NY.