Fig. 1: Tunability of zigzag graphene nanoribbon (ZGNR) edge states with twist angles and in-plane stacking offsets.

a Schematic of twisted bilayer zigzag graphene nanoribbon (TBZGNR) junctions with varying twist angles. Blue and black ribbons represent bottom and top layer ZGNRs, respectively (also in f). The angle θ represents the twist angle between the top and the bottom ribbon. Red shadow regions illustrate the edges of the top layer ZGNR within the overlapping region (also in f). b–e Density-functional-theory (DFT)-calculated projected density of states (PDOS) on the edge atoms in the red shadow regions in cases with several typical twist angles. In the case of a twist angle of 0°, both β-AB (solid curve) and AA stacking (dashed curve) are considered. The grey shading represents the PDOS for edge atoms in monolayer ZGNR. The results in c–e are based on structures with overlapping central hexagons, which are the most symmetric junctions. f Schematic of TBZGNR junctions with the same twist angle of 90° but different in-plane stacking offsets. Two typical stacking geometries are shown here for example. The yellow shadows highlight the moiré sites with AA stacking used for distinguishing different stacking configurations. g–i DFT-calculated PDOS of the edge atoms (within the red shadowed regions shown in f) in three typical TBZGNR stacking symmetries with the same twist angle of 90°. Insets show where the moiré sites are located. j–l DFT-calculated interlayer electrostatic potential (in the middle plane between the top and bottom GNRs) of three 90°-TBZGNRs with the atomic stackings shown in g–i. Here the interlayer distance is fixed at 3.0 Å for the calculation.