Disorder and screening in decoupled graphene on a metallic substrate

We report the coexistence of charge puddles and topographic ripples in graphene decoupled from the Ir(111) substrate it was grown on. We show the topographic and the charge disorder to be locally correlated as a result of the intercalation of molecular species. From the analysis of quasiparticle scattering interferences, we find a linear dispersion relation, demonstrating that graphene on a metal can recover its intrinsic electronic properties. The measured Fermi velocity $v_F=0.9\pm 0.04\times {10}^6$ m/s is lower than in graphene on dielectric substrates, pointing to a strong screening of electron-electron interactions in graphene by the nearby metallic substrate.

Figure 1

(a) Scanning tunneling micrograph on graphene on Ir(111). The image size is $400\times 400{\mathrm{nm}}^2$, the tunnel current is $I=1$ nA, and the bias voltage $V=0.57$ V). The atomic step in epitaxial Ir(111) covered by graphene is 2.5 Å  high. Inset: zoom-in $\left(2.3\times 2.3{\mathrm{nm}}^2\right)$ atomic resolution image, $I=1$ nA, $V=0.01$ V. (b) Local tunneling spectroscopy $G\left(V\right)=dI/dV$. The Dirac point $(eV=E_D$, arrow) is defined by the minimum of $G$.

Figure 2

(a) Dirac point map (color code) superimposed with a 3D plot of the long-wavelength topography. Image of $250\times 250{\mathrm{nm}}^2$. (b) Carrier density distribution extracted from (a) (see text). (c) Angular average ${\chi }_{z-E_D}\left(\right|\mathbf{r}\left|\right)$ of the cross-correlation function (see text) between the above $E_D$ and topography maps.

Figure 3

(a)–(f) $G(\mathbf{r},E)$ maps for $E=-185,15,125,345,555$, and 700 meV, respectively. The color scale is set to cover fluctuations of $\pm 25\%$ with respect to the average $G$ at a given $E$. As the Dirac point is approached, the islands size can no longer be resolved. (g) Power spectral density from angular averaging of Fourier transform of (b) (blue) and (c) (green). The inset shows the Fourier transform of (b). The scale bar is 0.$5{\mathrm{nm}}^{-1}$. (h) Energy–wave-vector relation extracted from Fourier analysis of the density of states maps at energy $E$. The dashed lines are fits to the linear dispersion relation of graphene, yielding $v_F=0.90\pm 0.04\times {10}^6$ m/s and $E_D^0=0.32$ eV.

Figure 4

Dirac point map at zero magnetic field (a) and at $B=2$ T (b). Density of states map at $E-E_D=-330$ meV at zero magnetic field (c) and $B=2$ T (d). All four maps are taken over the same region at $T=130$ mK.