Two-dimensional electron and hole gases at the surface of graphite

We report two-dimensional (2D) electron and hole gases induced at the surface of graphite by the electric field effect. The 2D gases reside within a few near-surface atomic layers and exhibit mobilities up to 15 000 and $60000{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$ at room and liquid-helium temperatures, respectively. The mobilities imply ballistic transport on $\mu \mathrm{m}$ scale. Pronounced Shubnikov–de Haas oscillations reveal the existence of two types of charge carries in both electron and hole gases.

Figure 1

(Color online) Electric field effect in graphite. Conductivity $\sigma$ as a function of gate voltage $V_{\mathrm{g}}$ for graphite films with $d\approx 5$ and $50\mathrm{nm}$ (main panel and upper inset, respectively); $T=300\mathrm{K}$. For the $5\mathrm{nm}$ device, $\mu \approx 11000$ and $8500{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$ for electrons and holes, respectively. Left inset: schematic view of our experimental devices. Right inset: optical photograph of one of them ($d\approx 5\mathrm{nm}$; the horizontal wire has a $5\mu \mathrm{m}$ width).

Figure 2

(Color online) Hall coefficient $R_{\mathrm{H}}$ as a function of $V_{\mathrm{g}}$ for the $5\mathrm{nm}$ device of Fig. 1. Inset: resistivity ${\rho }_{\mathrm{xy}}\left(B\right)$ for various gate voltages. From top to bottom, the plotted curves correspond to $V_{\mathrm{g}}=-30$, $-100$, $-2$, 100, and $20\mathrm{V}$. Close to zero $V_{\mathrm{g}}$, ${\rho }_{\mathrm{xy}}$ curves are practically flat indicating a compensated semimetal whereas negative (positive) $V_{\mathrm{g}}$ induce a large positive (negative) Hall effect. Solid curves in the main inset show the dependences $R_{\mathrm{H}}\propto n$ and $R_{\mathrm{H}}=1∕ne$ expected at low and high $V_{\mathrm{g}}$, respectively.

Figure 3

(Color online) SdH oscillations in a $5\text{−}\mathrm{nm}$ film at three gate voltages (main panel). Note that the frequency of SdH oscillations increases with increasing $V_{\mathrm{g}}$ (concentration of 2D electrons increases). The lower panel magnifies the oscillations for one of the voltages $(V_{\mathrm{g}}=90\mathrm{V})$ after subtracting a linear background. The inset shows an example of the SdH fan diagrams used in our analysis to find SdH frequencies. $N$ is the number associated with different oscillations’ minima.

Figure 4

(Color online) SdH frequencies $B_{\mathrm{F}}$ as a function of carrier concentration $n$. Different symbols indicate oscillations due to near surface carriers in different devices. The data for different samples were aligned along the $x$ axis so that zero $n$ corresponded to minimum $\sigma$, which takes into account the chemical shift. (Ref. 10) Solid lines are the best linear fits. The inset shows amplitude $\Delta \rho$ of SdH oscillations as a function of $T$ for 2D electrons and holes (open and solid symbols) at $B_{\mathrm{F}}=85$ and $55\mathrm{T}$, respectively. Solid curves are the best fits allowing us to find the carriers’ cyclotron masses.