Density functional calculations on the intricacies of Moiré patterns on graphite

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

“…Especially, the low-lying LLs anticross frequently, leading to the existences of non-well-behaved and perturbed LLs. The spatially dramatic changes of the LL wavefunctions in the anticrossings can be verified by scanning tunneling microscope (STM) measurements [57,58], as done for 2D electron gas [83] and topological insulators [84]. In this paper, the important differences among trilayer graphenes such as their energy band structures, LL splittings, LL ordering, and LL anticrossings, are investigated.…”

“…Few-and multi-layer graphenes have been successfully produced by experimental methods such as exfoliation of highly orientated pyrolytic graphite [55][56][57][58], metalorganic chemical vapour deposition (MOCVD) [61][62][63][64][65][66], chemical and electrochemical reduction of graphene oxide [67][68][69], and arc discharge [70,71]. There exist important stacking configurations, including AAB [57,58,69], ABC [59,60,[66][67][68][69], AAA [62,63], ABA [60,61,66,69], and twisted [62,69] and turbostratic ones [64]. The interlayer atomic interactions and stacking configurations induce the rich electronic properties of graphene.…”

“…The essential electronic properties can be drastically changed by the layer number [35][36][37], stacking configuration [37][38][39][40][41][42], magnetic field [43,44], electric field [45][46][47], dopping [48,49], mechanical strain [50][51][52], and temperature variation [53,54]. Few-and multi-layer graphenes have been successfully produced by experimental methods such as exfoliation of highly orientated pyrolytic graphite [55][56][57][58], metalorganic chemical vapour deposition (MOCVD) [61][62][63][64][65][66], chemical and electrochemical reduction of graphene oxide [67][68][69], and arc discharge [70,71]. There exist important stacking configurations, including AAB [57,58,69], ABC [59,60,[66][67][68][69], AAA …”

Electronic properties of twisted bilayer nanoribbons

“…Below a RRA of approximately 10 o , the Fermi velocity starts to diminish, and around a RRA of about 1 o the bands are completely flat [4,5]. For these low rotation angles, a moiré pattern in the density of states develops, and distinct stacking regions can be observed [4,5,19]. Regions with AA and AB stacking can be distinguished, whereas others seem to be built of displaced graphene layers, called for this reason slip regions.…”

“…We build the unit cell of the twisted bilayer nanoribbon (TBNR) starting from a unit cell (UC) of a commensurate TBG [18,19], which in turn is obtained by rotating a Bernal-stacked bilayer. The rotation axis passes through a B site, which has an atom in a layer situated at the center of a hexagon of the other layer.…”