Magic-angle semimetals

Understand

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.