Quantum oscillations of the two-dimensional hole gas at atomically flat diamond surfaces

Shubnikov–de Haas oscillations are observed in atomically flat hydrogen-terminated diamond surfaces with high-density hole carriers introduced by the electric field effect using an ionic liquid. The Shubnikov–de Haas oscillations depend only on the magnetic field component perpendicular to the diamond surface, thus providing evidence of two-dimensional Fermi surfaces. The effective masses estimated from the temperature dependence of the oscillations are close to the cyclotron effective masses of the valence band maxima in diamond. The estimated quantum scattering time is one order of magnitude longer than the transport scattering time and indicates that the carrier mobility is locally as high as several thousand cm${}^2$/V s at low temperature.

Figure 1

(a) Atomic force microscope image of an atomically flat (111) diamond surface with steps and terraces. This is the central part of the device shown in Fig. 1. (b) Hall bar on the top surface of a mesa with a lateral dimension of $\approx 40\times 40$ $\mu$m; the top surface of the mesa is atomically flat as shown in Fig. 1. The surface of the Hall bar, which is used as the channel of an ionic liquid-gate transistor, is hydrogen terminated. The area other than the Hall bar is covered with Al${}_2$O${}_3$ for insulation. (c) Schematic diagram of the whole device. The blue line represents the hydrogen-terminated diamond surface, while the red line represents the oxygen-terminated diamond surface. A small amount of ionic liquid is applied between the diamond surface and gate electrode. (d) Temperature dependence of the sheet resistance of the device channel at $V_g=0$ and $-1.4$ V.

Figure 2

(a)Magnetic field ($B$) dependence of the sheet resistance $R_s$ measured for $V_g=-1.4$ V at $T=0.50–1.71$ K by applying a magnetic field perpendicular to the diamond surface. (b) Plot of $d{R}_s/d(1/B)$ as a function of $1/B$. The curves except for $T=0.50$ K are offset vertically for clarity. (c) The Fourier spectra of the oscillations shown in Fig. 2 in the range $1/B=0.125–0.3$ (1/T). Arrows indicate peaks at $F=21$, 43, 63, and 81 T. (d) Plot of the peak intensity at $F=43$ T of the Fourier spectra [Fig. 2] as a function of temperature. The fit yields the effective mass $m^{*}/m_0=0.66\pm 0.03$. Inset: The bottom curve is $d{R}_{\mathrm{s}}/d(1/B)$ as a function of $1/B$ at $T=0.50$ K, which is the same as that shown in (b). The top curve was constructed as the sum of the oscillations for $F=21$, 43, 63, and 81 T calculated using Eq. (1) to provide a fit to the bottom curve, which determined a Dingle temperature of 1.8 K.

Figure 3

(a) Magnetic field ($B$) dependence of the sheet resistance $R_s$ of another device measured for $V_g=-4$ V at $T=0.51–1.68$ K by applying a magnetic field perpendicular to the (111) diamond surface. We note that this device was fabricated with a different lithography process from those described in Sec. 2. For example, electrical contacts to the channel were made with TiC, which was produced by the deposition and annealing of Ti. Hall and resistance measurements lead to $n_{\mathrm{Hall}}=4.8\times {10}^{13}$ cm${}^{-2}$ and ${\mu }_{\mathrm{Hall}}=52$ cm${}^2$/V s at $T=0.50$ K. (b) Plot of the oscillatory component of the magnetoresistance as a function of $1/B$. The curves except for $T=0.51$ K are offset vertically for clarity. (c) The Fourier spectra of the oscillations shown in (b) in the range $1/B=0.833–0.4$ (1/T). Arrows indicate peaks at $F=7.9$ and 18 T. (d) Plot of the peak intensity at $F=7.9$ and 18 T of the Fourier spectra (c) as a function of temperature. The fits yield the effective mass $m^{*}/m_0=0.68\pm 0.08$ (7.9 T) and $0.77\pm 0.08$ (18 T).

Figure 4

(a) Magnetic field dependence of resistance of a device (that is different from those shown in Figs. 2 and 3) measured for $V_g=-1.8$ V at 2.0 K for different magnetic field orientations. The field is perpendicular to the (111) diamond surface at $\theta =0^{\circ }$ and parallel to it at $\theta ={90}^{\circ }$. The curves except for $\theta =-2^{\circ }$ are offset vertically for clarity. Hall and resistance measurements lead to $n_{\mathrm{Hall}}=5.7\times {10}^{13}$ cm${}^{-2}$ and ${\mu }_{\mathrm{Hall}}=52$ cm${}^2$/V s at $T=2.0$ K. (b) The same data in Fig. 4 plotted as a function of $Bcos\theta$. The curves except for $\theta =-2^{\circ }$ are offset vertically for clarity. The dashed lines are a guide to the eye. The inset shows the oscillatory components of the curves shown in Fig. 4 as a function of $1/Bcos\theta$.