Jedediah Pixley, PhD, Rutgers University,
Assistant Professor,
Department of Physics and Astronomy

The ability to control and manipulate the strength of correlations in quantum matter is one of the central questions in condensed matter physics today. While pressure, chemical doping, or magnetic field have served as conventional tuning knobs for a wide class of correlated systems, the ability to twist van der Waals materials has recently emerged as a novel scheme to engineer strong correlations and tune electronic properties. In the case of twisting two sheets of graphene, at a particular "magic-angle", the kinetic energy of electronic degrees of freedom is expected to vanish, and as a result, interaction effects should dominate. This has now been demonstrated experimentally following the recent discovery of superconductivity in close proximity to correlated insulating phases in magic-angle graphene. These results have now been reproduced by a number of experimental groups and extended to other two-dimensional van der Waals materials.

In this talk, I will discuss our theory that describes the magic-angle phenomena as a universal property of Dirac points in an incommensurate potential. As a result, we will discuss the generalization of the magic-angle effect to a wide class of models and distinct physical settings, such as ultra-cold atomic gases, trapped ions, and metamaterials. It will be shown that the magic-angle in twisted bilayer graphene is, in fact, a single particle quantum phase transition that can be described by a delocalization transition in momentum space with multifractal wavefunctions akin to electrons in a magnetic field and the celebrated Hofstadter's butterfly. The effects of correlations will be considered by constructing effective Hubbard models with dramatically enhanced interactions due to this novel quantum phase transition.