Fractal patterns in superconductors could lead to new energy technologies

The world is currently facing a critical point in meeting its energy demands due to the challenges posed by powering the technological age. This has prompted a growing need for the development of superconductors that can operate under ambient pressure and temperature, which would significantly contribute to solving the ongoing energy crisis.

The progress in superconductivity heavily relies on advancements in quantum materials. Within these materials, when electrons undergo a phase transition, they can form intricate patterns known as fractals. Fractals are never-ending patterns that exhibit self-similarity when zoomed in. Common examples of fractals include tree structures or frost on a windowpane during winter. Fractals can exist in two dimensions, such as frost on a window, or in three-dimensional space, like the branches of a tree.

Dr. Erica Carlson, a distinguished physicist and astronomer holding the position of 150th Anniversary Professor of Physics and Astronomy at Purdue University, has led a team of researchers in developing theoretical techniques to characterize the fractal shapes created by electrons within quantum materials. This research aims to uncover the underlying physics behind these intricate patterns.

Through her work, Dr. Carlson has analyzed high-resolution images depicting the electron distributions in a superconductor called Bi2-xPbzSr2-yLayCuO6+x (BSCO). Her findings confirm that these images indeed exhibit fractal properties and extend throughout the entire three-dimensional space occupied by the material, resembling a tree filling the space.

What was previously considered as random arrangements within the fractal images has turned out to be purposeful and surprisingly not caused by an anticipated underlying quantum phase transition. Instead, the patterns are a result of a phase transition induced by disorder within the material.

Dr. Carlson has collaborated with researchers from various institutions to publish their findings titled “Critical nematic correlations throughout the superconducting doping range in Bi2-xPbzSr2-yLayCuO6+x” in the scientific journal Nature Communications.

The collaborative team includes scientists from Purdue University, including Dr. Forrest Simmons, a recent Ph.D. graduate, and former Ph.D. students Dr. Shuo Liu and Dr. Benjamin Phillabaum. The research conducted by the Purdue team was carried out under the umbrella of the Purdue Quantum Science and Engineering Institute (PQSEI). The team also comprises researchers from partner institutions, namely Dr. Jennifer Hoffman, Dr. Can-Li Song, and Dr. Elizabeth Main from Harvard University, Dr. Karin Dahmen from the University of Urbana-Champaign, and Dr. Eric Hudson from Pennsylvania State University.

Dr. Steven Kivelson, a distinguished theoretical physicist specializing in novel electronic states in quantum materials and the Prabhu Goel Family Professor at Stanford University, acknowledges the significance of Dr. Carlson and her collaborators’ observation of fractal patterns of orientational domains in cuprate high-temperature superconductors. According to Dr. Kivelson, this observation is not only aesthetically appealing but also of fundamental importance in understanding the underlying physics of these materials.

Nematic order, which is often considered an indicator of a more primitive charge-density-wave order, has been suggested to play a crucial role in cuprate theory. However, previous evidence supporting this proposition has been inconclusive. The analysis conducted by Carlson and her team provides two important insights:

The fractal nature of the observed nematic domains implies that the correlation length, which represents the distance over which nematic order remains coherent, is much larger than the experimental field of view, indicating its significant scale compared to other microscopic dimensions.

The similarity between the observed patterns and those obtained from studies of the three-dimensional random-field Ising model, a renowned model in classical statistical mechanics, suggests that the extent of nematic order is influenced by extrinsic factors. In the absence of crystalline imperfections, it is expected to exhibit even longer-range correlations extending deep into the bulk of the crystal, not just along the surface.

High-resolution images of these fractal patterns are painstakingly obtained in the labs of Dr. Jennifer Hoffman at Harvard University and Dr. Eric Hudson, now at Penn State, using scanning tunneling microscopes (STM). The STM scans the surface of the cuprate superconductor, BSCO, atom by atom. The surprising finding was that the orientations of the electronic stripes exhibited two different directions instead of a uniform direction, resulting in a jagged image with intriguing patterns.

According to Dr. Carlson, the electronic patterns are complex, featuring nested holes and intricate filigree-like edges. Fractal mathematics techniques are employed to characterize these shapes using fractal numbers. Additionally, statistical methods derived from phase transitions are used to analyze factors such as the size distribution of clusters and the likelihood of sites belonging to the same cluster.

Upon analyzing these patterns, the Carlson group made a surprising discovery. These patterns are not limited to the surface but rather fill three-dimensional space. Simulations to explore this finding were conducted at Purdue University, utilizing the institution’s supercomputers at the Rosen Center for Advanced Computing. The measurements were performed on samples with five different doping levels by researchers at Harvard and Penn State, and the observed behavior remained consistent across all five samples.

The collaboration between Illinois, led by Dr. Karin Dahmen, and Purdue, led by Dr. Erica Carlson, has brought cluster techniques from disordered statistical mechanics into the realm of quantum materials, particularly superconductors. Carlson’s team successfully adapted these techniques to study quantum materials, thereby expanding the understanding of second-order phase transitions to encompass electronic fractals in these materials.

This advancement represents a significant step towards unraveling the mysteries of cuprate superconductors. Cuprates are currently the highest-temperature superconductors that operate under ambient pressure. Achieving superconductivity at such conditions would greatly contribute to solving the energy crisis since the wires used in electronics are typically made of metals that incur energy losses during current transmission. Unlike metals, superconductors can carry current without any energy dissipation. Additionally, superconductors possess the ability to generate high magnetic fields and enable magnetic levitation. They are currently employed, albeit with extensive cooling systems, in MRI machines and levitating trains.

Moving forward, the Carlson group plans to extend the Carlson-Dahmen cluster techniques to investigate other quantum materials.

“We have also discovered electronic fractals in other quantum materials, such as vanadium dioxide (VO2) and neodymium nickelates (NdNiO3), using these cluster techniques,” Carlson reveals. “We suspect that this behavior might be quite prevalent in various quantum materials.”

Such discoveries bring quantum scientists closer to unraveling the enigma of superconductivity.

“The broader field of quantum materials aims to explore the quantum properties of materials and harness them for technological advancements,” explains Carlson. “With each new quantum material discovered or created, we gain new capabilities, analogous to painters discovering new colors to incorporate into their palette.”

Source: Purdue University

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