Twisting quantum matter beyond the graphene paradigm

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 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 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