Moiré Flat Bands in Twisted Double Bilayer Graphene

Abstract

We investigate twisted double bilayer graphene (TDBG), a four-layer system composed of two AB-stacked graphene bilayers rotated with respect to each other by a small angle. Our ab initio band structure calculations reveal a considerable energy gap at the charge point neutrality that we assign to the intrinsic symmetric polarization (ISP). We then introduce the ISP effect into the tight-binding parameterization and perform calculations on TDBG models that include lattice relaxation effects down to very small twist angles. We identify a narrow region around the magic angle θ • = 1.3 • characterized by a manifold of remarkably flat bands gapped out from other states even without external electric fields. To understand the fundamental origin of the magic angle in TDBG, we construct a continuum model that points to a hidden mathematical link to the twisted bilayer graphene (TBG) model, thus indicating that the band flattening is a fundamental feature of TDBG, and is not a result of external fields.

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

“…The electronic structure of small magic angle twisted bilayer graphene features four flat bands lying around the Fermi level, with band splitting at the point of the Brillouin zone of the emergent moiré superlattice [10,42]. Density functional theory (DFT) calculations have shown results consistent with those effective models in twisted graphene multilayers, yet quantitative modifications are observed when including relaxation of the atomic coordinates [29,30,[43][44][45] and crystal-field effects [34,46]. Therefore, to benchmark the electronic properties of twisted graphene multilayers, it is essential to start from a correct description that takes into account the geometric corrugation and ab initio electrostatics of the moiré system.…”

Pairing in graphene-based moiré superlattices

“…The most recent member of the family of strongly correlated graphene superlattice systems is twisted double bilayer graphene [51][52][53], where two individually aligned ABstacked graphene bilayers are twisted with respect to one another. As theoretical calculations show [54][55][56][57][58][59][60], flat electronic bands can be realized by tuning the twist angle and a vertical electric field. Similar to the above-mentioned graphene moiré systems, both correlated insulating [51][52][53] and superconducting [51,52] phases are observed in experiment.…”

Ultraheavy and Ultrarelativistic Dirac Quasiparticles in Sandwiched Graphenes

“…In particular, effectively 2D heterostructures consisting of flat sheets of graphene, transition metal dichalcogenides, and hexagonal boron nitride have been successful candidates for the moiré-induced correlated phenomena. [13][14][15][16][17][18][19][20][21][22][23] Recent experimental progress in studying correlations in multilayer heterostructures with more than two twisted graphene layers 13, 24-26 has led to a search for novel multilayer platforms with a particular focus on the trilayer geometry. 14,[27][28][29][30] In this work, we provide a detailed ab initio study of a unique extension of the TBG system: the twisted graphene sandwich (Fig.…”