Figure 1

(a) (Inset) Schematic of the device structure used. An atomically thin sheet of h-BN separates the top gate from graphene. An adjacent lead $i$ is used to extract the current $I$ that travels from the top gate (biased by $V_{\mathrm{T}}$) to graphene. A voltage $V_{\mathrm{G}}$ is applied on the back gate to control the sheet density ($n_s$) in graphene. (main) The tunnel conductance $g$ as a function of $\sqrt{n_s}$ measured at $V_{\mathrm{T}}=0$ and temperature of 4 K. Dashed lines are guides to the eye. (b) $g$ measured as a function of $V_{\mathrm{T}}$ for $V_{\mathrm{G}}=0$.Reuse & Permissions

Figure 2

(a) $g(V_{\mathrm{T}},V_{\mathrm{G}})$ shows a suppression of $g$ for the values of $V_{\mathrm{T}}$ and $V_{\mathrm{G}}$ outlined by white dashed lines. (b) (Inset) Simulation of $\delta g(V_{\mathrm{T}},V_{\mathrm{G}})$ in arbitrary units. (Main) $\delta g(V_{\mathrm{T}},V_{\mathrm{G}})$ measured for device A. Parabolic curves (black dashed lines) correspond to constant-density-of-states contours. In addition, a collection of $V_{\mathrm{G}}$-independent peaks are observed (one is highlighted by the dotted line). Squares indicate two unexplained features in $\delta g$ that are likely due to tunneling enhanced by an impurity adjacent to the graphene sheet. (c) $\delta g$ averaged over all positive values of $V_{\mathrm{G}}$ show the $V_{\mathrm{G}}$-independent peaks apparent in (a) and (b). Arrows correspond to the voltages 10, 32, 68, 90 mV, from left to right.Reuse & Permissions

Figure 3

(a) Cut of $g\left(V_{\mathrm{T}}\right)$ at $V_{\mathrm{G}}=-10$ V for device B. showing a suppression of $g$ for values of $V_{\mathrm{T}}$ less than $\sim$70 mV. (b) $g(V_{\mathrm{T}},V_{\mathrm{G}})$ shows the threshold of 70 mV is independent of $V_{\mathrm{G}}$ for the range $-50$  to 20 V. (c) Inelastic tunneling spectroscopy, measured by $\delta g$ and averaged over the entire $V_{\mathrm{G}}$ range, shows peaks at 10, 40, 66, 84 mV (shown by arrows for positive $V_{\mathrm{T}}$ but also apparent for negative values of $V_{\mathrm{T}}$). (d) Peaks in $\delta g$ are $V_{\mathrm{G}}$-independent for the range $-50$  to 20 V.Reuse & Permissions

Figure 4

$g$ for smaller values of $V_{\mathrm{T}}$ for (a) device A and (b) device B. Diamond-like features are attributed to charge puddle formations in the graphene sheet for each device. Coulomb blockade features are more pronounced in device B.Reuse & Permissions