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. For example, when two sheets of graphene are twisted to a "magic angle," the kinetic energy of the electronic degrees of freedom vanishes and, as a result, interaction effects dominate. This has now been demonstrated experimentally following the recent discovery of superconductivity in close proximity to correlated insulating phases in magic-angle graphene.
In this talk, I will first discuss our theory that describes the magic-angle phenomena as a universal property of Dirac points in an incommensurate potential. This allows us to generalize the magic-angle effect to a wide class of models and distinct physical settings, such as ultra-cold atomic gases, trapped ions, and metamaterials. This general perspective will then be used to demonstrate how the surface states of topological insulators and unconventional superconductors can be manipulated via a twist. These results will then be applied to describe recent experiments on twisted slabs of the high-temperature superconductor Bi2Sr2CaCu2O8+y.