Magic-angle semimetals

TL;DR

This paper introduces the concept of magic-angle semimetals, where incommensurate effects induce a quantum phase transition characterized by flat bands, multifractality, and delocalization, with potential realization in ultracold gases.

Contribution

It demonstrates that the magic-angle effect can be modeled as a single-particle quantum phase transition across various systems, extending the concept beyond twisted bilayer graphene.

Findings

Nonanalytic density of states at criticality

Presence of flat bands and multifractal wave functions

Delocalization in momentum space and divergent interaction scales

Abstract

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.