Abstract
Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré 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.
Highlights
The engineering of band structures with non-trivial topological wave functions has achieved success in creating and controlling quantum phases in a variety of systems such as doped semiconductors[1,2,3,4], ultracold atoms[5,6], and metamaterials[7,8]
As a consequence of the quenched kinetic energy, correlations dominate the physics and exotic many-body states may form. This interpretation relies on the reduction of the electronic velocity and large increase of the density of states (DOS) which was shown in twisted bilayer graphene (TBG) theoretically[16,17,18,19] and experimentally[20,21,22] prior to the recent groundbreaking discoveries in refs. 9–11
We develop the theory for twistronic emulators by first distilling the basic physical phenomena that create correlated flat bands out of two-dimensional Dirac cones
Summary
The engineering of band structures with non-trivial topological wave functions has achieved success in creating and controlling quantum phases in a variety of systems such as doped semiconductors[1,2,3,4], ultracold atoms[5,6], and metamaterials[7,8]. The form of the wave functions is completely different in the metallic state, see Fig. 3c, d, as it appears delocalized both in momentum and real space with non-trivial structure (see details in Supplementary Note 5). Throughout the metallic phase the spectra appear to be weakly multifractal in both momentum and real space (Supplementary Note 5), we find for the SOC model that τM(q) ≈ 2(q − 1) − 0.25q(q − 1) and for the cTBG model we obtain τM(q) ≈ 2(q − 1) − 0.15q(q − 1) (in the npj Quantum Materials (2020) 71.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
