Two-dimensional Dirac fermions in thin films of $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$

Two-dimensional states in confined thin films of the three-dimensional Dirac semimetal $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ are probed by transport and capacitance measurements under applied magnetic and electric fields. The results establish the two-dimensional Dirac electronic spectrum of these states. We observe signatures of $p$-type conduction in the two-dimensional states as the Fermi level is tuned across their charge neutrality point and the presence of a zero-energy Landau level, all of which indicate topologically nontrivial states. The resistance at the charge neutrality point is approximately $h/e^2$ and increases rapidly under the application of a magnetic field. The results open many possibilities for gate-tunable topological devices and for the exploration of novel physics in the zero-energy Landau level.

Figure 1

Magnetoresistance and quantum Hall effect of samples A and B (with gate dielectric). (a) $R_{xx}$ and $R_{xy}$ as a function of magnetic field, showing SdH oscillations in $R_{xx}$ and incipient quantum Hall plateaus in $R_{xy}$. (b) Landau fan diagrams. (c) SdH oscillations after background subtraction. Lifting of the twofold degeneracy can be seen above 9 T for sample A but not sample B.

Figure 2

Magnetotransport behavior of the gated devices. (a) $R_{xx}$ of sample A as a function of gate bias $\left(V_{\mathrm{g}}\right)$ for different magnetic fields. (b) $|e{R}_{\mathrm{H}}{|}^{-1}$ extracted from the low-field Hall effect as a function of $V_{\mathrm{g}}$ for sample A. (c) and (d) $R_{xy}$ of samples A and B, respectively, as a function of the magnetic field, for large negative values of $V_{\mathrm{g}}$ (Fermi level below the CNP of the two-dimensional states). Data were anti-symmetrized using the relation $[R_{xy}\left(B\right)-R_{xy}\left(-B\right)]/2$, to suppress contributions from the noise and intermixing of $R_{xx}$ and $R_{xy}$ signals. The inset in (b) shows a schematic of the gated Hall bar structure (bottom) and sketches that illustrate the tuning of the Fermi level (dashed line) with respect to the two-dimensional states (blue) at different $V_{\mathrm{g}}$. Bulk states are shown in gold.

Figure 3

SdH oscillations as a function of $V_{\mathrm{g}}$ for sample A. (a) $R_{xx}$ as a function of $V_{\mathrm{g}}$ at 14 T. Landau level indices of the minima are indicated. (b) Magnetic field behavior of the SdH oscillations, offset for clarity. Data were symmetrized using the relation $[R_{xx}\left(B\right)+R_{xx}\left(-B\right)]/2$.

Figure 4

Fan diagram. (a) Plot of $\frac{d^2\log R_{xx}}{d{V}_{\mathrm{g}}^2}$ (arbitrary units) as a function of $B$ and $V_{\mathrm{g}}$ for sample A. A smoothing procedure prior to each differentiation was performed to increase the signal to noise ratio. (b) Position of the maxima in (a), as extracted with a peak finding algorithm, as a function of the carrier density $n_{\mathrm{H}}$, determined from the Hall effect, as shown in Fig. 2. (c) Same data as in (b), but plotted as $\nu B$, where ν is the filling factor, which collapse on a single straight line. Labels in (a) and (b) indicate the Landau level $N$.

Figure 5

$C\text{−}V$ characteristics. (a) Capacitance of sample A measured as a function of gate voltage with and without an applied magnetic field of 14 T. (b) Quantum capacitance extracted from the data shown in (a), as a function of the square root of the modulated carrier density. The dotted lines are a fit to the data at zero magnetic field.