Strong correlations in magic-angle semimetals

In magic-angle graphene, Moiré patterns lead to an enlarged unit cell, mini-Brillouin zone, and strongly correlated phases (as shown experimentally). We generalize this behavior to a whole class of semimetallic models from one- to three-dimensions, and we show that the key ingredients are (1) an “untwisted” semimetallic band structure and (2) a spatially quasiperiodic structure (e.g., a “twist”) [1]. As the quasiperiodic structure is enhanced, the velocity of the effective low-energy semimetal decreases until it vanishes at a quantum phase transition. The magic-angle phenomena are associated with this eigenstate phase transition which is a unique type of “Anderson delocalization” transition in momentum space. Further, it is accompanied with flat-bands and behaves universally across models. Lastly, we build effective Hubbard models on the new bands by computing Wannier states. The interactions in these Hubbard models are strongly enhanced at this transition, indicating the existence of strongly correlated phases. All ingredients to realize our proposal are available in present-day cold-atomic laboratories for which the magic-angle effect can be exploited to induce strong correlations in quantum degenerate gases.

[1] Fu, Yixing et al., arXiv:1809.04604 (2018).