Advancements in Fractal Mathematics Could Help Solve the World’s Energy Crisis

Meeting the world’s energy demands is becoming increasingly difficult. As we continue to power our technological age, we are faced with the global energy crisis. The development of superconductors that can operate at ambient pressure and temperature could go a long way toward solving this problem.

Quantum Materials and Fractals

Advancements in superconductivity are linked to advances in quantum materials. When electrons within quantum materials undergo a phase transition, they can form intricate patterns, including fractals, which are never-ending patterns. Fractals can form in two dimensions, such as frost on a window, or in three-dimensional space, like the limbs of a tree.

Research Findings

Dr. Erica Carlson, a 150th Anniversary Professor of Physics and Astronomy at Purdue University, has led a team of researchers that developed theoretical techniques for characterizing fractal shapes formed by electrons within a superconductor. They discovered that the fractals extend into the full three-dimensional space occupied by the material. What was once thought to be random dispersions within the fractal images are purposeful and due to a disorder-driven phase transition.

The research team, which includes Dr. Carlson, evaluated high-resolution images of the locations of electrons in a superconductor and determined that they are indeed fractal. They published their findings in Nature Communications.

Potential Applications

Superconductors carry current perfectly with no loss of energy, unlike metals used in current wires. Superconductors can also generate high magnetic fields and are used in MRIs in hospitals and levitating trains. The development of superconductors that work at ambient pressure and temperature could go a long way toward solving the energy crisis.

Future Research

Using the Carlson-Dahmen cluster techniques, the research team has identified electronic fractals in other quantum materials, including vanadium dioxide and neodymium nickelates. This type of discovery leads quantum scientists closer to solving the riddles of superconductivity and gaining new capabilities in the field of quantum materials.