(a) Schematic of the experimental setup for tunneling spectroscopy in 2LG; (b) energy diagrams at the tunnel junction are shown for zero applied bias , where the 2LG is initially gapped and charge neutral (), (c) electron-doped (), and (d) hole-doped (). The initial conditions depend on the work function difference between the probe electrode and 2LG, initial doping due to impurities, and back gate voltage .
Energy band diagrams of (a) a charge-neutral (shown in Fig. 1(b)) and (b) an hole-doped (shown in Fig. 1(c)) 2LG planar tunnel junction with finite applied bias . The effects of (2LG is positively biased) on the Fermi level and energy band gap are shown for both positive and negative initial perpendicular displacement fields as indicated. The red dashed lines mark the Fermi level in 2LG, shifted due to bias-induced charging. At the far right, a cartoon of the expected tunneling conductance vs. is shown for each case, where grey dashed lines mark the “measured” positions of band edges.
Numerical simulation of tunneling conductance (red) and its derivative (blue) for a 2LG planar tunnel junction. Here, back-gate voltage sets the Fermi level to the charge neutrality point, initial energy gap , and the bias-induced charging factor .
a) Schematic of the fabrication of a lithography-free tunnel junction on 2LG. The cylindrical quartz filament allows subsequent angled deposition of aluminum and (b) titanium/gold to fabricate, with oxidation of the aluminum, a tunnel junction on one side of the filament; (c) optical image of a quartz filament atop a bilayer graphene flake prior to depositions; (d) resistance R, measured between the two Au contacts, vs. gate voltage for a typical device.
a) Optical image of a completed 3-point 2LG planar tunnel junction prepared lithographically; (b) schematic of the device shown in (a); (c) atomic force microscopy image of an alumina () film grown on 2LG supported by a substrate by depositing a 2 nm-thick Al film at 77 K; (d) tunneling conductance of a 2LG planar tunnel junction for = 0, measured at T = 10 K.
a) Tunneling spectra (smoothed and shifted) vs. bias voltage in a 2LG tunneling device, prepared with a filament shadow mask, measured at T = 10 K for fixed back gate voltages in steps of 1 V; (b) tunneling conductance for = 51 V for applied perpendicular magnetic fields of H = 0 and 8 T; (c) map of tunneling conductance (smoothed) vs. and for H = 8 T). Dashed lines highlight the shifting positions of the conductance peaks annotated in (b).
Tunneling spectra (smoothed and shifted) vs. bias in a 2LG tunnel junction, prepared photolithographically, measured at T = 10 K for fixed back gate voltages .
a) Calculated (smoothed) from measurements of a 2LG planar tunnel junction at = 28 V and T = 10 K; (b) numerically simulated and smoothed , with prominent peaks fit to those of (a); (c) tunneling bias at which the μ = 0 is accessed, , vs. total charge carrier density .
Bilayer band gap displacement field D as measured in a 2LG tunnel junction. Total charge carrier density indicated by color. The dashed line denotes the linear dependence of on D with = 0. Inset: vs. .
a) Optical image of a 2LG (outlined) transport device prior to depositions of top gate dielectric and electrode; (b) schematic of a 2LG FET with a top and back gate (TG and BG); (c) resistance per square □ back gate voltage () for fixed top gate voltages ; (d) maximum resistance vs. inverse temperature . Dashed lines indicate simple thermal activation fits at high temperature. Inset: Band gap , extracted from simple thermal activation trends at high temperature, vs. perpendicular field D. Colors in the main panel and inset correspond to labeled in (c).
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