Magnetoresistance oscillations arising from edge-localized electrons in low-defect graphene antidot-lattices
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(Color online) (a) Schematic view of a honeycomb-like GADL, which shows the situation where the boundaries are aligned with the carbon hexagonal lattice of graphene to form a zigzag edge. Narrow spaces between two ADs correspond to GNRs with width W. The actual structure has a larger number of hexagonal carbon unit cells per GNR (length∼40 nm and W∼20 nm). This GADL provides at least three large advantages (see supplementary material (2)).21 (b) AFM image of GADL formed using an etching mask with mean AD diameter φ ∼ 80 nm and W ∼20 nm. (c) MFM image of an H-terminated GADL. A CoPtCr-coated Si probe was used for measurements in tapping mode. The inter-AD regions, which exhibit darker color, imply a high density of polarized spins. In particular, evidence for AD-edge-localized spins may be seen in the parts shown by the arrows. (d)(e) Typical Raman spectra of a GADL (d) prior and (e) after annealing at 800 °C, taken with a laser excitation of 532 nm and 0.14 mW incident power at room temperature. Because the laser beam diameter φ used for the measurement is 1 µm, the result reflects edge information from ∼60 ADs. Inset of (e) distribution of I(D)/I(G) in 8 samples. 15 points at 5 different positions were observed per sample. Dotted and solid lines above and below 0.5 denote I(D)/I(G) prior and after annealing, respectively. Black and open symbols correspond to the main panels of (d) and (e), respectively.
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(a) Schematic views of electron trajectories under magnetic fields and the unit cells in a honeycomb-like GADL (see supplementary material (6)). (b) MR (ρxx) measurements of the hydrogen-terminated ∼10-layer GADL (with a mean φ ∼80 nm and mean a ∼150 nm, implying an aspect ratio φ/a ∼0.5) as a function of B applied perpendicular to the GADL at T = 1.5 K. Measurements were performed by a standard low-frequency (13 Hz) ac lock-in technique using a constant excitation current of 1 nA. (c) (d) Fourier power spectra of sample in (b) for (c) low B and (d) high B regions.
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