Emulating twisted double bilayer graphene with a multiorbital optical lattice

TL;DR

This paper proposes a theoretical method to emulate twisted double bilayer graphene using ultracold atoms in multiorbital optical lattices, revealing flat bands and magic-angle phenomena analogous to those in graphene.

Contribution

It introduces a novel approach to simulate twisted bilayer graphene physics with ultracold atoms, including the emergence of flat bands and magic-angle conditions.

Findings

Identification of magic-angle conditions with flat bands

Observation of Anderson-like delocalization transition in momentum space

Perturbative description of miniband formation and flat bands

Abstract

This work theoretically explores how to emulate twisted double bilayer graphene with ultracold atoms in multiorbital optical lattices. In particular, the quadratic band touching of Bernal stacked bilayer graphene is emulated using a square optical lattice with $p_x$, $p_y$, and $d_{x^2-y^2}$ orbitals on each site, while the effects of a twist are captured through the application of an incommensurate potential. The quadratic band touching is stable until the system undergoes an Anderson like delocalization transition in momentum space, which occurs concomitantly with a strongly renormalized single particle spectrum inducing flat bands, which is a generalization of the magic-angle condition realized in Dirac semimetals. The band structure is described perturbatively in the quasiperiodic potential strength, which captures miniband formation and the existence of magic-angles that qualitatively agrees with the exact numerical results in the appropriate regime. We identify several magic-angle conditions that can either have part or all of the quadratic band touching point become flat. In each case, these are accompanied by a diverging density of states and the delocalization of plane wave eigenstates. It is discussed how these transitions and phases can be observed in ultracold atom experiments.