Recently, condensed matter physics has been captivated by a series of experiments showing unconventional superconductivity and correlated insulating states in a system called twisted bilayer graphene. This system is composed of two sheets of graphene, carefully stacked on top of each other but physically twisted with respect to one another. Experimental breakthroughs have allowed precision control of the angle between sheets, revealing superconductivity and other correlated states appear at small twist angles (around 1 degree). With a whole body of experiments now confirming and extending the initial results, a frontier of materials are being looked at for similar effects, broadly called moiré materials.
The understanding of the physics of moiré materials relies on the geometry of the twist. Instead of merely a lattice of atoms, a pattern forms, creating a large “supercell” which quenches the kinetic energy and leads to strong correlations. Such structures have a long history in physics from the quantum Hall effect and Hofstadter’s butterfly to twisted bilayer graphene. In this talk, we will go over some of this history, making connections back to twisted bilayer graphene and going further: uncovering a class of models we call “magic-angle semimetals.” Many different ideas in modern-day condensed matter physics find harbor here: from topology, to Anderson-like localization transitions, and even to strong correlations.