Magic-angle semimetals

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.

Emulating twisted double bilayer graphene with a multiorbital optical lattice

“…Interestingly, the perturbative expressions show that it is possible for the renormalized masses to diverge, signalling the generation of flat bands. This is thus the natural extension of the concept of the "magic-angle condition" suitably generalized for Dirac semimetals [14] to the QBT case. This is also consistent with the notion of a magic-angle in twisted double bilayer graphene in the absence of trigonal warping and particle hole asymmetric perturbations [40].…”

“…Here, we use the full H 0 (k) in Eq. ( 3) and include the quasiperiodic potential H V as a perturbation using diagrammatic perturbation theory [14]. After formally performing the perturbative calculation, we expand our results near the QBT point up to second order in q ≡ k−(π, π), and thus the resulting theory is only valid near the QBT point.…”

“…For example, the QBT broken state remains largely extended when Q/2π = 1/2 because for this Q the potential is V (r) = W [cos(πx + φ x ) + cos(πy + φ y )], which simply quadruples the unitcell (a factor of 2 from each directions) and nothing else. For these commensurate Q's there is no delocaization in momentum space (as I k is then bounded from below due to Bloch's theorem [14]). Similar, but less prominent situations are observed in Q/2π = 1/3, 1/4, • • • as well.…”

“…Guided by similar studies of Dirac semimetals [14,15,48] in incommensurate potentials we examine the IPR in real and momentum space. The stability of the QBT to quasiperiodicity implies a stable plane wave eigenstate at the QBT energy that is localized in momentum space, i.e., I k (E QBT ) ∼ const.…”

“…On the other hand, recent developments in the ability to accurately twist van der Waals heterostructures [7][8][9][10][11] have opened the door for a new level of control over two-dimensional solid-state materials. Recent theoretical work has proposed realizations of this phenomena in ultracold atomic systems by either twisting the optical lattice [12] or its spin state [13], as well as emulating the effects of a twist using incommensurate, quasiperiodic potentials [14][15][16][17][18]. Recently, experiments have successfully twisted optical lattices holding a Bose-Einstein condensate opening the door for experimental realizations of twistronics of ultracold atoms [19].…”