Prof. Luiz Santos awarded DOE grant for “Catalyzing Chiral Quantum Matter at Hofstadter Van Hove Singularities”

Fractals are patterns with strikingly beautiful self-similar behavior across different scales. Besides governing the shapes of galaxies, continents, and grains of sand, fractality and self-similarity are present in the quantum spectrum of electrons in two-dimensional lattices subject to a perpendicular magnetic field. Fractal Hofstadter bands have revolutionized the understanding of topology in quantum physics, but their rich structures remain mostly associated with quantum Hall phenomena. Prof. Santos’ goal is to unleash the full potential of fractal Hofstadter bands, and to establish them as platforms to catalyze new interacting quantum phenomena, such as pairing of electrons in fractal bands under large magnetic flux and novel topological quantum critical phenomena. The vision is to establish a framework for studying quantum chiral matter by controlling a rich landscape of tunable, self-similar Van Hove singularities that are unique to such systems.

The proposed research launches transformative concepts broadly impacting the field of interacting topological systems, by proposing electronic band fractality as a design principle to achieve exotic quantum orders. It addresses fundamental questions that could forge new connections among topological phases of matter, unconventional superconductivity, and quantum information sciences.