Atomic corrugation and electron localization due to Moiré patterns in twisted bilayer graphenes

Model for the metal-insulator transition in graphene superlattices and beyond

“…However, conflicting results are found on the gap at point between these lowest bands and higher-energy bands when the twist angle is small. Some numerical calculations report relatively large gaps of 10 − 20 meV on both electron and hole sides [11], while others show that the gap only exists on the electron side [17] or even no gap exists [13,15,18].…”

“…This is, however, a nontrivial task that has not been accomplished so far. Thanks to extensive studies using various methods [6,[11][12][13][14][15][16][17][18][19][20][21][22][23], the band structure of TBG at small twist angle is known to be rather complex and depends sensitively on microscopic details such as lattice relaxation. Near the socalled magic twist angle, various methods find four nearly flat minibands at low energy, but differ significantly on important features such as their bandwidth and the gap to excited bands.…”

Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite

“…• has been recently reported [20]. For the case of very small angles, a full DFT based minimization of the lattice was not performed in view of the diverging size of the supercell.…”

Twistronics: Manipulating the electronic properties of two-dimensional layered structures through their twist angle

“…The resulting structures may have commensurate stacking for special orientations, but more generally are incommensurate. This allows for interesting new behavior: studies of bilayer graphene have found clear twist-dependent features in both the electronic density of states and the conductivity 10,11 ; at very small twist-angles, a domain-wall phase appears, related to the stacking configuration 12 . Similar effects may occur in TMDC semiconductors, with their band-gaps affected by the substrate and the relative twist-angle orientation 13 .…”

“…In the effort to capture the physics of incommensurate systems, a simple approximation is to consider large super-cells that can mimic the incommensurate system; in the case of first-principles calculations like density functional theory (DFT), that can afford relatively small cells, this approximation limits the physical system rather severely to special values of the twist angle 11 . This leaves important questions unaddressed: Are there distinct physical characteristics that distinguish the incommensurate from the commensurate case?…”