Electrostatic modulation of the electronic properties of Dirac semimetal ${\mathrm{Na}}_3\mathrm{Bi}$ thin films

Large-area thin films of topological Dirac semimetal ${\mathrm{Na}}_3\mathrm{Bi}$ are grown on amorphous ${\mathrm{SiO}}_2$:Si substrates to realize a field-effect transistor with the doped Si acting as a back gate. As-grown films show charge carrier mobilities exceeding 7 $000{\mathrm{cm}}^2$/V s and carrier densities below $3\times {10}^{18}{\mathrm{cm}}^{-3}$, comparable to the best thin-film ${\mathrm{Na}}_3\mathrm{Bi}$. An ambipolar field effect and minimum conductivity are observed, characteristic of Dirac electronic systems. The results are quantitatively understood within a model of disorder-induced charge inhomogeneity in topological Dirac semimetals. The hole mobility is significantly larger than the electron mobility in ${\mathrm{Na}}_3\mathrm{Bi}$ which we ascribe to the inverted band structure. When present, these holes dominate the transport properties.

Figure 1

(a) Device schematic, showing Hall bar film geometry defined by the surface stencil mask affixed on the ${\mathrm{SiO}}_2$ on Si substrate that serves as a back gate. After growth of the ${\mathrm{Na}}_3\mathrm{Bi}$ thin film, the molecular charge acceptor F4-TCNQ is subsequently deposited on the top surface. (b) STM morphology of sample. Scan area is $50\times 50$ nm (vertical color scale nm), STM bias voltage ${\mathrm{V}}_{\mathrm{bias}}=-300$ mV, and current $I=200$ pA. The observable step edges have heights of 4.2 Å, close to the expected 4.83 Å half-unit cell [3].

Figure 2

(a) Zero field conductivity (S/cm) and (b) low-field Hall carrier density $\left({10}^{18}{\mathrm{cm}}^{-3}\right)$ vs back-gate voltage $\left({\mathrm{V}}_g\right)$, for the ${\mathrm{Na}}_3\mathrm{Bi}$ film as grown (blue circles), and after the deposition of 8.8 Å  F4-TCNQ on the surface (solid squares).

Figure 3

(a) Gate dependence of the zero-field resistivity ${\rho }_{xx}$ $(\mathrm{\Omega }$ cm) after top-gating with F4-TCNQ. The red points are the measured values; the blue line is the theoretical fit. (b) Transverse magnetoresistance ${\rho }_{xy}$ as a function of magnetic field perpendicular to the film, for back-gate voltages $\left({\mathrm{V}}_g\right)$ indicated in the legend. The markers are the measured data, while the solid lines are fits using the charge inhomogeneity theory described in the text.

Figure 4

Carrier density $n$ as a function of gate voltage $V_{\mathrm{g}}$ for the as-grown sample as determined from Hall effect (blue circles) and for the F4-TCNQ-doped sample from the EMT fits in Fig. 3 (red squares). The solid green line is the value of the global fit parameter $n_{\mathrm{rms}}=2.2\times {10}^{17}{\mathrm{cm}}^{-3}$. The blue circles are the as-grown carrier density for comparison.