Figure 1

(a) $dI/dV$ and $d^{2}I/d{V}^2$ spectra of graphene monolayer on ${\mathrm{SiO}}_2$ with $V_g=+20\mathrm{V}$ (junction parameters: 0.5 V, 0.12 nA, $T=4.2\mathrm{K}$). Black arrow indicates minimum in $dI/dV$ due to Dirac point (corresponding point in $d^{2}I/d{V}^2$ is shown with gray dot). Inset: STM topograph showing typical graphene surface quality for this study. (b) $d^{2}I/d{V}^2$ measurements taken at same point on the graphene surface for different gate voltages ($V_g$) (junction parameters: $\pm 0.5\mathrm{V}$, 0.12 nA, 4.2 K). Non-carrier-density-dependent features are tracked with dashed colored lines. Carrier-density-dependent features are labeled D1, D2, and D3, and are tracked with solid colored lines.Reuse & Permissions

Figure 2

(a) Green line shows theoretical elastic tunneling conductance ($dI/dV$) of graphene with no many-body interactions present. Blue line shows theoretical elastic component of $dI/dV$ for graphene including many-body interactions. Red line shows total theoretical $dI/dV$ for graphene including both elastic and inelastic tunneling processes. The blue curve and the green curve have been multiplied by a factor of 7 for easier viewing; all three curves share a common origin. Inset: Calculated $\mathrm{Im}\Sigma (\epsilon )$ for graphene quasiparticles along the $\Gamma \mathrm{\text{−}}K$ direction due to $e\mathrm{\text{−}}e$ (red line) and $e\mathrm{\text{−}}\mathrm{ph}$ (blue line) interactions. (b) Solid line shows normalized theoretical $d^{2}I/d{V}^2$ for graphene including both elastic and inelastic processes as in (a). Dotted line shows experimental $d^{2}I/d{V}^2$ measurement of graphene with $V_g=+20\mathrm{V}$ (corresponding to $n=18\times {10}^{11}{\mathrm{cm}}^{-2}$ used in the theoretical calculation).Reuse & Permissions

Figure 3

Comparison between (a) experimental and (b) theoretical $d^{2}I/d{V}^2$ versus sample bias in the filled states of graphene for different gate voltages ($V_g$) and corresponding electron densities (experimental junction parameters: $-0.5\mathrm{V}$, 0.12 nA, 4.2 K). Dispersive features D1’ and D2’ in (b) are known to arise from electron-plasmon interactions, while dispersive feature D3’ is known to arise from electron-phonon interactions (dispersive features are tracked with solid colored lines as a guide to the eye). Nondispersive features in (b) (tracked with dashed colored lines as a guide to the eye) are known to arise from phonon-mediated inelastic tunneling channels. Solid gray dots mark the position of the Dirac point ($V_D$) for different gate voltages [Fig. 3a] and corresponding electron densities [Fig. 3b].Reuse & Permissions