Local Gating of an Ir(111) Surface Resonance by Graphene Islands

The influence of graphene islands on the electronic structure of the Ir(111) surface is investigated. Scanning tunneling spectroscopy (STS) indicates the presence of a two-dimensional electron gas with a binding energy of $-160\mathrm{meV}$ and an effective mass of $-0.18m_e$ underneath single-layer graphene on the Ir(111) surface. Density functional calculations reveal that the STS features are predominantly due to a holelike surface resonance of the Ir(111) substrate. Nanometer-sized graphene islands act as local gates, which shift and confine the surface resonance.

Figure 1

Main figure: Spectra of $dI/dV/(I/V)$ recorded along a line from Ir onto a graphene island as indicated in Inset (b). A clear shift of the surface resonance onset occurs. Contours of constant LDOS calculated using a scattering model (see text) are indicated by black and light gray lines for Ir and graphene, respectively. A horizontal blue (gray) line indicates the position of the graphene edge. Inset (a): Spectra of $dI/dV$ recorded near the beginning [blue (black)] and end [red (dark gray)] of the line in Inset (b). The beginning of the line is defined by the cross at the dotted line in Inset (b). Inset (b): Constant-current STM image of a graphene patch on Ir(111) ($-220\mathrm{mV}$, 100 pA). White dots mark positions where $dI/dV$ spectra were recorded. A white cross denotes zero distance. The false colors used in the main figure and in Inset (b) are defined in the upper-right-hand corner.

Figure 2

Calculated band structures of (a) pristine and (b) graphene-covered Ir(111). Light gray lines in (a) show the dispersion of all states of the supercell used. The contribution of each state to the tunneling current is indicated by the widths of blue (black) and red (dark gray) lines. On Ir, the current is essentially due to a surface resonance at the center of the surface Brillouin zone ($\overline{\Gamma }$). On the graphene-covered surface, the resonance is shifted upwards. It still carries most of the current, while the Dirac cone around $\overline{K}$ is less conducting. Green (gray) parabolas show a fit with an effective mass $m^{*}\approx -0.17m_e$.

Figure 3

(a) Constant-current STM image of a graphene island on Ir(111) ($-220\mathrm{mV}$, 1 nA). A blue (light gray) circle indicates the effective island diameter of 8.3 nm used for further analysis. (b)–(d) Normalized $dI/dV$ maps of the graphene island in (a), recorded at the indicated voltages. The observed LDOS oscillations evolve as expected for the confinement of an electron gas in a quantum dot. (e) Energies of confined states with significant LDOS at the island center ($n=0$) measured from various graphene islands. States with $l=1$ (open blue circles) and $l=2$ (filled red circles) are resolved. Lines show a fit according to Eq. (2) with $E_0=-160\mathrm{meV}$ and $m^{*}=-0.18m_e$, which are in good agreement with values calculated within DFT.

Figure 4

Spatially resolved normalized $dI/dV$ spectra recorded along a line through a graphene island (inset). The experimental distance scale was recalibrated to account for the small curvature of the measurement path. Light gray lines mark contours of constant LDOS calculated for the circular island which is indicated in the inset. Blue (gray) lines indicate the boundaries of the model island. Inset: Constant-current STM image of the graphene island ($-220\mathrm{mV}$, 100 pA). White dots indicate positions where spectra of $dI/dV$ were recorded. A white ring denotes zero distance. An inscribed blue (gray) circle shows the effective island diameter of 11.8 nm used in modeling.