Quantum oscillations and quantum Hall effect in epitaxial graphene

We investigate the transport properties of high-quality single-layer graphene, epitaxially grown on a 6H-SiC(0001) substrate. We have measured transport properties, in particular charge-carrier density, mobility, conductivity, and magnetoconductance of large samples as well as submicrometer-sized Hall bars which are entirely lying on atomically flat substrate terraces. The results display high mobilities, independent of sample size. The temperature dependence of the conductance indicates a rather strong coupling to the SiC substrate. An analysis of the Shubnikov-de Haas effect yields the Landau-level spectrum of single-layer graphene. When gated close to the Dirac point, the mobility increases substantially and the graphenelike quantum Hall effect occurs.

Figure 1

(Color) Scanning electron micrograph of a Hall bar ($0.48\mu \text{m}$ width) lithographically patterned out of a single layer of graphene (dark blue) on an atomically flat substrate terrace of semi-insulating SiC. The substrate steps are clearly resolved.

Figure 2

(Color) (a) and (b) Histograms of charge-carrier density $n$ and charge-carrier mobility $\mu$ in epitaxial graphene for 51 samples of various sizes at room temperature. Both quantities have been determined by Hall effect measurements. (c) Temperature dependence of resistivity $\rho$ and mobility $\mu$ of a typical Hall bar sample. The resistivity increases superlinearly with increasing $T$, while $\mu$ decreases linearly.

Figure 3

(Color) Resistance $R_{xx}$ and Hall resistance $R_{xy}$ at $T=4.2\text{K}$ from a sample of single-sheet graphene, entirely placed on a single substrate step (Fig. 1). $R_{xx}$ shows Shubnikov-de Haas oscillations, but no quantum Hall effect. The Hall resistance, however, shows steplike plateaus such as in the quantum Hall effect. Plateau values and the positions of extrema can be identified with the unconventional Landau-level structure of single-layer graphene.

Figure 4

(Color) Landau-level index $n$ of the SdH maxima (closed symbols) and minima (open symbols) over the inverse magnetic field $1/B$ and linear fits. Circles: as-prepared sample lying on a single substrate terrace. Squares: as-prepared sample covering several substrate steps. Triangles: sample gated close to charge neutrality with F4-TCNQ (plotted against $0.1/B$ for clarity). Inset: the axis intercepts of $\beta =0.5$ and $\beta =0$ for minima and maxima, respectively, yield a Berry phase of $\pi$ as expected for single-layer graphene. The error bars indicate the standard deviation of the fitting constant.

Figure 5

(Color) Charge-carrier mobility $\mu$ and density $n$ for a sample close to the charge neutrality point $\left(E_F=27\text{meV}\right)$. Closed symbols: $\mu$ (red) and $n$ (blue) derived from an evaluation of Hall data, assuming only one charge-carrier type, yields mobilities of $29000{\text{cm}}^2/\text{Vs}$. The strong temperature dependence comes from the interplay of electrons and holes in the Fermi distribution at finite temperatures. A simple two-band model (open squares) yields a similar $T$ dependence. Open symbols: the same sample after exposure to air for six days $\left(E_F=59\text{meV}\right)$ (open squares). We attribute the higher $n$ and reduced $\mu$ to the degradation of the F4-TCNQ layer.

Figure 6

(Color) XPS spectra of a sample before and after application of F4-TCNQ molecules. In the survey spectrum (a) additional $\text{F}1s$ an $\text{N}1s$ peaks are found after evaporation of F4-TCNQ (spectra shifted for clarity). A closer look to the $\text{C}1s$ peak (b) shows signals of the SiC substrate (SiC) and the BL. The shift of the graphene peak (g) due to the F4-TCNQ doping is clearly visible.

Figure 7

(Color) Resistance $R_{xx}$ and Hall resistance $R_{xy}$ at $T=4.2\text{K}$ in a sample doped close to charge neutrality by F4-TCNQ. (a) Shubnikov-de Haas oscillations (barely visible below 4 T) and quantum Hall effect are present and demonstrate the unique single-layer graphene properties. Due to a lost wire $R_{xx}$ was measured on day 1 in a three-terminal geometry (see inset). Contact and wiring give rise to an additional resistance of $\approx 300\Omega$. $R_{xy}$, however, is measured correctly. (b) The same sample with repaired contact wire measured during the following days. Day 2 (solid line) and day 3 (dashed line) show that for high $B$ $R_{xx}$ becomes essentially zero. Additional peaks arise in $R_{xx}$, probably due to increasing inhomogeneities. Day 4 (dashed-dotted line) shows data after rinsing the sample in water. The inhomogeneities become more pronounced but QHE effect is still visible for $B>26\text{T}$.