Topology and the Renormalization Group (RG) are powerful concepts guiding our understanding of modern materials. Topology classifies emerging properties robust to local perturbations seen in a host of latest quantum materials. RG monitors changes in physical behavior according to the scale of observation, providing a framework to characterize universal behavior near phase transitions.
Bringing these two motifs to bear, Prof. Luiz Santos’ group has unveiled a scenario for unconventional superconductivity in two dimensional crystals subject to a perpendicular magnetic field. While these magnetic crystals are known to support fractal electronic bands originally proposed by Hofstadter and recently realized in moire’ heterostructures and cold atomic lattices, the properties of topological Hofstadter bands have been much associated with the quantum Hall effect. However, his group has investigated a rather unexplored feature of these quantum fractals, which is the presence of singular hotspots where electronic states interact strongly, allowing new collective behavior to emerg. Thier RG analysis of electronic states near the singularities uncovers new attractive channels between electrons that enable the onset of Hofstadter Superconductors displaying topological edge modes. These findings highlight Hofstadter materials as a promising route to achieve topological superconductors that could have future applications in quantum computation.