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(a) Top view of a pair of arbitrarily oriented graphene monolayers (layer 2, red and layer 1, blue) in a two-layer stack. (b) A two-layer stack on top of a (gray/light gray) wafer, etched and contacted (yellow) for transport measurements.
(a) Optical image of the two-layer sample before and after etching. (b) The resistivity (black) and the conductivity (red dots) plotted vs the back-gate voltage applied between silicon substrate and graphene. (c) The AFM image of the edge showing two steps (red arrows) and (d) its averaged height profile.
(a) Longitudinal resistance measured as a function of a perpendicular magnetic field for . The upper figure shows the oscillation corresponding to the lower carrier concentration ; the zoomed part in the bottom panel shows the oscillations corresponding to the high concentration, . (b) Same plots for . (c) Comparable measurement on a SC bilayer showing only one sequence of oscillations with typical bilayer behavior. (d) Two carrier concentrations in the two-layer (folded) graphene sample extracted from the period of the SdH oscillations. The boxes mark the points obtained using the data shown in panels (a) and (b). The black lines are the results of the theoretical modeling of the device. A shift in the gate voltage of 11.5 V takes into account doping of graphene by deposits.
(a) Schematic of the second sample used in the experiment. The graphene layer and the top-gate metallic plate are separated via a PMMA layer. A current was driven through the source-drain contacts (yellow) while the longitudinal resistance was measured. The two layers are marked in red (layer 2) and blue (layer 1). (b) Image of the sample showing the etched flake, the contacts, and the top gate. The edges of the flake and of the top gate are highlighted using dashed lines. (c) Longitudinal resistance vs back-gate voltage for . The maxima in the resistance correspond to the two neutrality points underneath the top gate (red arrow) and outside the gated region (green arrow). Using the shift with gate voltages, one obtains a ratio of 2.5 between the capacitive couplings of the flake to the top and back gates. (d) Two-dimensional plot showing vs the inverse magnetic field and the top-gate voltage at . Different sets of SdH oscillations can be seen. Traces for two different top-gate voltages ( and ) are depicted in (e) and (f), showing maxima at for both oscillations.
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