Emulating twisted double bilayer graphene with a multiorbital optical lattice

We theoretically explore how to emulate twisted double bilayer graphene with ultracold atoms in multiorbital optical lattices. In particular, the quadratic band touching (QBT) of Bernal stacked bilayer graphene is emulated using an optical lattice with p_x, p_y, and d_x²−y² orbitals on each site, while the effects of a twist are captured through the application of an incommensurate potential. The QBT is stable while the system undergoes an Anderson-like delocalization transition in momentum space and re-enters the QBT phase, which occurs concomitantly with a strongly renormalized single-particle spectrum. The band structure is described perturbatively in the quasiperiodic potential strength where the transition is indicated by the diverging effective mass, which agrees well with the exact numerical results for a weak potential strength.