Imaging charge density fluctuations in graphene using Coulomb blockade spectroscopy

Using scanning tunneling microscopy (STM), we have imaged local charge density fluctuations in monolayer graphene. By placing a small gold nanoparticle on the end of the STM tip, a charge sensor is created. By raster scanning the tip over the surface and using Coulomb blockade spectroscopy, we map the local potential on the graphene. We observe a series of electron and hole doped puddles with a characteristic length scale of $~$20 nm. Theoretical calculations for the correlation length of the puddles based on the number of impurities are in agreement with our measurements.

Figure 1

(a) Schematic of the graphene sample with gold contacts on a SiO${}_2$ substrate. The nanoparticle at the tip apex is shown in the closeup sketch. (b) Optical microscope image of the monolayer graphene flake and gold electrodes. (c) Large-scale STM image of the graphene surface. ($V_t=-0.5$ V, $I_t=100$ pA, $100\hspace{0.5em}\text{nm}\times 100\hspace{0.5em}\text{nm}$). The scale bar is 20 nm. (d) STM image showing the atomic resolution of the hexagonal lattice of monolayer graphene ($V_t=-0.5$ V, $I_t=100$ pA, $7\hspace{0.5em}\text{nm}\times 7\hspace{0.5em}\text{nm}$). The scale bar is 1.4 nm.

Figure 2

(a) $\mathit{dI}/\mathit{dV}$ point spectroscopy showing peaks due to the addition of individual electrons to the nanoparticle. (b) $\mathit{dI}/\mathit{dV}$ spectroscopy as a function of tip voltage and gate voltage, showing a series of Coulomb blockade diamonds. This demonstrates that the nanoparticle on the end of the tip acts as a quantum dot. This data set was taken at a different location from the curve shown in (a). (c) $\mathit{dI}/\mathit{dV}$ curves taken at two different points on the graphene surface. Each shows a series of peaks but they are horizontally offset due to the different potential on the graphene surface. (d) Distribution of peak spacings for a $100\hspace{0.5em}\text{nm}\times 100\hspace{0.5em}\text{nm}$ area of the graphene film. The peaks are clustered around the same value, showing that there is a single quantum dot located on the end of the tip. Set point parameters are $V_t=-0.5$ V, $I_t=100$ pA for (a)–(c), and $V_g=0$ V for (a), (c), and (d).

Figure 3

Local density of states maps taken at a series of tip voltages as indicated for each map. Each map is $100\hspace{0.5em}\text{nm}\times 100\hspace{0.5em}\text{nm}$. Set point parameters are $V_t=-0.5$ V, $I_t=100$ pA, $V_g=0$ V. A ring is circled to show how it changes with energy. They start out circular (a), (b) and slowly become asymmetric (c)–(e). Then a second ring forms (f) at the same location once the charge on the nanoparticle changes by one.

Figure 4

Potential fluctuations in the same $100\hspace{0.5em}\text{nm}\times 100\hspace{0.5em}\text{nm}$ region of the flake as in Fig. 3. Red areas have positive potential while blue areas are negative.

Figure 5

(a) Correlation length for the puddles shown in Fig. 4. (b) Resistivity as a function of gate voltage for the graphene flake measured at 4.6 K.