Abstract

We introduce and characterize a class of magic-angle semimetal models and, as an application, propose multiple cold atomic quantum emulators of twisted bilayer graphene. The models are defined in one to three dimensions and all contain momentum space nodes as well as an incommensurate quasiperiodic potential. With both numerical and analytical tools, we demonstrate an undiscovered link between magic-angle phenomena and a single-particle eigenstate quantum phase transition. At criticality, we numerically report a nonanalytic behavior of the density of states, the appearance of flatbands, and wave functions which Anderson delocalize in momentum space displaying a multifractal scaling spectrum. Preliminary analytical large N calculations which corroborate part of the numerical results will also be discussed. We outline the necessary conditions for magic-angle semimetals and construct effective Hubbard models on superlattices by computing Wannier states, which demonstrates that the effective interaction scale is dramatically enhanced across the single-particle transition. As a result, we argue that the eigenstate quantum criticality is unstable towards the inclusion of interactions.