Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moir\'e pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold-atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models "magic-angle semimetals." Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.
@article{arxiv.1809.04604,
title = {Magic-angle semimetals},
author = {Yixing Fu and E. J. König and J. H. Wilson and Yang-Zhi Chou and J. H. Pixley},
journal= {arXiv preprint arXiv:1809.04604},
year = {2020}
}