Dirac materials, such as graphene and topological insulators, have attracted substantial attention owing to their unique band structures and appealing physical properties originated from two-dimensional (2D) Dirac fermions with linear energy dispersion.1, 2, 3, 4 Recently, the existence of three-dimensional (3D) Dirac fermions has been theoretically predicted while several potential candidates, including β-BiO2,5 Na3Bi6 and Cd3As27 were explored as topological Dirac semimetals (TDSs), in which the Dirac nodes are developed via the point contact of conduction-valence bands. By breaking certain symmetries, 3D TDSs could be driven into various novel phases, such as Weyl semimetals,6, 7, 8 topological insulators,7, 8 axion and band insulators,6, 8, 9, 10 thus providing a versatile platform for detecting unusual states and exploring numerous topological phase transitions.

Among 3D TDSs, Cd3As2 is considered to be an excellent material owing to its chemical stability against oxidation and extremely high mobility.11, 12, 13, 14 Although the electrical, thermal and optical properties of Cd3As2 have been widely investigated, hampered by the complicated crystal structure its band structure remains a matter of controversy.14, 15 Recently, first-principle calculations have revealed the nature of 3D topological Dirac semimetal state in Cd3As2.2, 7, 8 Soon after the prediction, its inverted band structure with the presence of Dirac fermions was experimentally confirmed.11, 13, 16, 17, 18, 19 More importantly, beyond the relativistic transport of electrons in bulk Cd3As2, a theoretically predicted topological insulator phase may eventually emerge upon the breaking of crystal symmetry.7 Furthermore, thickness-dependent quantum oscillations could be anticipated to arise from arc-like surface states.20 Such perspective manifests the superiority of Cd3As2 thin films for the study of the quantum spin Hall effect and the exploration of unconventional surface states in the Dirac semimetals.

Previously, amorphous and crystalline Cd3As2 films were prepared on various substrates by thermal deposition,21, 22, 23 showing Shubnikov–de Haas (SdH) oscillations and a quantum size effect.24, 25, 26 However, despite the extensive studies in the past, synthetized Cd3As2 always exhibits n-type conductivity with a high electron concentration, therefore calling for a well-controlled growth scheme and the tunability of carrier density.14, 27 Theory proposed that the chiral anomaly in TDSs can induce nonlocal transport, especially with a large Fermi velocity when the Fermi level, EF, is close to the Dirac nodes.28 Hence, the ability to modulate the carrier density and EF in Cd3As2 has a vital role for the study of the transport behavior and TDS-related phase transitions. In view of preserving high mobility in Cd3As2, the electrostatic doping is an advantageous choice owing to its tunable and defect-free nature compared with the chemical doping.

To modulate a large-area flat film on an insulating substrate, an electric-double-layer transistor configuration was adopted because of its easy device fabrication and high efficiency in tuning the Fermi level, from which a high concentration of carriers can be accumulated on the surface to induce an extremely large electric field.29, 30, 31, 32, 33, 34 In this study, we demonstrate the tunable transport properties, including ambipolar effect and quantum oscillations of wafer-scale Cd3As2 thin films, deposited on mica substrates by molecular beam epitaxy (see Material and methods). Our transport measurements reveal a semiconductor-like temperature-dependent resistance in the pristine thin films. Taking advantage of the ionic gating, we are able to tune the Fermi level into the conduction band with a sheet carrier density, ns, up to 1013 cm−2 and witness an evident transition from band conduction to hopping conduction. Moreover, in a certain range of Fermi energy, tunable SdH oscillations emerge at low temperatures, and a transition from electron- to hole-dominated two-carrier transport is achieved by applying negative gate voltage, a strong indication of ambipolar effect, thus demonstrating the great potential of Cd3As2 thin films in electronic and optical applications.

Materials and methods

Sample growth

Cd3As2 thin films were grown in a Perkin Elmer (Waltham, MA, USA) 425B molecular beam epitaxy system. Cd3As2 bulk material (99.9999%, American Elements Inc., Los Angeles, CA, USA) was directly evaporated onto 2-inch mica substrates by a Knudsen cell. Freshly cleaved mica substrates were annealed at 300 °C for 30 min to remove the molecule absorption. During the growth process, the substrate temperature was kept at 170 °C. The entire growth was in situ monitored by the reflection high-energy electron diffraction (RHEED) system.

Characterizations of crystal structure of Cd3As2

The crystal structure was determined by X-ray diffraction (Bruker D8 Discovery, Bruker Inc., Billerica, MA, USA) and high-resolution transmission electron microscopy (HRTEM, JEOL 2100F, JEOL Inc., Tokyo, Japan) using a field emission gun. The TEM instrument was operated at 200 KV at room temperature.

Device fabrication

The thin films were patterned into standard Hall bar geometry manually. The solid electrolyte was made as follows: LiClO4 (Sigma Aldrich, St Louis, MO, USA) and poly (ethylene oxide) (Mw=100 000, Sigma Aldrich) powders were mixed with anhydrous methanol (Alfa Aesar, Ward Hill, MA, USA). The solution was stirred overnight at 70 °C and served as the electrolyte. After the application of solid electrolyte, the device was kept at 350 K for 30 min in vacuum to remove the moisture before the transport measurements.

Device characterizations

The magneto-transport measurements were performed in a Physical Property Measurement System by Quantum Design with a magnetic field up to 9 T. A home-made measurement system, including lock-in amplifiers (Stanford Research 830, Stanford Research Systems, Sunnyvale, CA, USA) and Agilent 2912 source meters (Keysight Technologies, Santa Rosa, CA, USA), was used to acquire experimental data.

Band structure calculations

Density functional theory-based first-principle calculations were performed for bulk Cd3As2. The resulting bulk Hamiltonian was projected onto a basis of Cd 5s and As 4p states, using wannier functions.35 The Cd 5s orbitals were rigidly shifted by 0.4 eV to match HSE calculations. This ab-initio-derived tight-binding Hamiltonian was then employed to study the system in slab geometries along the [001] direction. Because of the interest here in bulk features, that is, the evolution of the bulk gap, [001] oriented films were studied for simplicity and qualitative differences for [112] oriented films are not expected. Very recently, Cd3As2 has been shown to crystallize into the I41/acd space group (which is a supercell of the P42/nmc unit cell).15 However, the difference in the band structures for the two cells is minimal, and the smaller P42/nmc cell for Cd3As2 was used to perform the simulations. Density functional theory computations were performed using Vienna Ab-initio Simulation Package,36 including spin-orbit coupling. The Perdew–Burke–Ernzerhof parameterization to the exchange-correlation functional was used.37 A plane wave cutoff of 600 eV was employed, along with a 6 × 6 × 3 Monkhorst–Pack k-grid.

Results and discussion

TEM was carried out to characterize the crystal structure of Cd3As2. A typical selected-area electron diffraction pattern taken from the same area as the HRTEM image confirms the single crystallinity with the growth face of (112) plane, as shown in Figure 1a and inset. The atom columns cleaving from the original crystal cell mode (Figure 1e) along (112) plane agree well with that in the HRTEM image (Figure 1b). The surface morphology of the as-grown thin films was probed by atomic force microscopy with a root mean square of ~0.3 nm (Figure 1c). The atomically flat surface is consistent with the 2D growth mode reflected by the streaky RHEED pattern (Figure 1c inset), thus ensuring an ideal solid–liquid interface during the ionic gating process. The top surface can be identified as a series of {112} planes by X-ray diffraction (Figure 1d), which further confirms the TEM observations.

Figure 1
figure 1

Characterizations of as-grown Cd3As2 thin films. (a) A typical HRTEM image of Cd3As2 thin films, revealing a single crystalline structure. Inset: selected-area electron diffraction pattern. (b) The amplified image in the red box in panel (a) perfectly agreeing with the atom columns cleaving from the original crystal cell mode of Cd3As2 in panel (e) along (112) plane. (c) AFM image of the thin film surface. The RMS was determined to be ~0.3 nm. Inset: in-situ RHEED pattern during growth. (d) XRD spectrum. The marked peaks are the typical XRD patterns from Cd3As2 with a (112) plane of sample surface, while other peaks come from the mica substrate. (e) Simulated crystal structure of Cd3As2.

To carry out low-temperature transport measurements, a ~50-nm-thick Cd3As2 thin film was patterned into a standard Hall bar configuration with a channel dimension of 2 × 1 mm2. A small area of the isolated thin film was left around the channel to serve as a gate electrode. After examining the properties of the pristine sample, a droplet of solid electrolyte was deposited on the device surface to cover the channel area (see Figure 2a). Figure 2b shows the temperature-dependent resistance Rxx of the pristine Cd3As2 thin film prior to the ionic gating process. The negative dRxx/dT suggests semiconducting behavior that is different from the metallic nature of the bulk counterpart.12, 19 The activation energy (Ea) is extracted to be 12.45 meV by fitting the Arrhenius plot of Rxx at high temperature (from 280 to 350 K) with the equation Rxx~exp(Ea/kBT), where kB is the Boltzmann constant and T is the measurement temperature. The band gap, Egap, is roughly estimated to be >24.9 meV from Ea, which is reasonable for the Cd3As2 thin film of this thickness. The sheet carrier density, ns, at 2 K is determined to be 1.5 × 1012 cm−2 by Hall effect measurements. Such a low carrier density, along with the semiconducting characteristics, indicates that the Fermi level is located inside the bandgap in pristine Cd3As2 thin films.

Figure 2
figure 2

Electric transport of ~50-nm-thick Cd3As2 thin film with solid electrolyte gating. (a) A schematic view of solid electrolyte gated Cd3As2 device structure. The inset shows the geometrical configuration of the magnetic field. (b) Temperature-dependent longitude resistance Rxx of Cd3As2 before the application of the solid electrolyte. Inset: the Arrhenius plot of Rxx. (c) Temperature-dependent Rxx with different positive gate voltages VG, displaying a gate-induced metallic behavior. (d) Temperature-dependent Rxx of gated Cd3As2 Hall bar device with different negative gate voltage VG. The gate-induced hole accumulation in n-type Cd3As2 results in semiconducting-like Rxx-T behavior. The dashed curve here represents the fitting of the hopping conduction at low temperatures. (e) The electronic band structure of the Cd3As2 thin film with a thickness of ~50 nm.

With ionic gating, we can efficiently tune the Fermi level in order to achieve two-carrier transport in Cd3As2. Several as-grown Cd3As2 thin films have been measured (Supplementary Section SI; Supplementary Figures S1–S4, Supplementary Figures S12–S17 and Supplementary Table SI). Under positive gate voltage (0<VG<0.5 V, Figure 2c), Rxx shows a negative temperature dependence, indicative of a semiconducting state. Increasing VG up to 1.2 V, a metallic behavior is witnessed by a change of negative- to positive-temperature dependence. This behavior originates from the fact that the Fermi level has been moved into the conduction band (VG0.5 V, Figure 2c). However, when VG becomes negative, Rxx shows a completely negative-temperature dependence without metallic behavior owing to the insufficient hole doping (Figure 2d). Interestingly, the hopping conduction at low temperatures has been observed in this regime, as indicated by the dashed line in Figure 2d. Note that the RxxT curves cross each other at about 50–150 K, suggesting that the Fermi level is closer to the valence band than to the conduction band in this critical temperature range. This gives rise to a hole-dominated transport at low temperatures, which will be investigated in the following section on magneto-transport. The bandgap opening behavior here shows a good agreement with our first-principle calculations. Figure 2e displays the calculated band structure of a typical Cd3As2 thin film with a thickness of ~50 nm. The bulk Dirac cone is fully opened, with a sizable gap >20 meV. This gap falls off with increasing thickness and is very close to zero for a thin film of thickness ~60 nm (see Supplementary Section SVIII). This variation in the bulk gap is in reasonable agreement with our experimental results.

In order to further study the gate-tunable RxxT behavior and ascertain the carrier type, magneto-transport measurements were carried out at low temperatures. A clear Hall anomaly at different VG was observed (see Figures 3a–d). According to the Kohler’s rule,38, 39, 40

Figure 3
figure 3

Temperature- and gate-dependent Hall resistance Rxy of ~50-nm-thick Cd3As2 thin film. (a) Rxy under −0.5 V (gate voltage), indicative of electron-dominated n-type conductivity. (b) Rxy under −0.6 V, showing a nonlinear behavior originated from two-carrier transport owing to the gate-induced holes. (c) Rxy under −0.9 V. The Cd3As2 channel undergoes a transition from electron- to hole-dominated transport as evidenced by the change of slope at B3 T. (d) Rxy under −2.2 V. The holes are dominant in Hall resistance. (e) Gate-dependent sheet carrier density. It implies the ambipolar transport. The hole carrier density was extracted from the fits to the two-carrier transport model. Electron carrier density was obtained from the Hall effect measurements. The graduated background represents the amount and type of carriers, blue for holes and red for electrons. (f) Temperature-dependent conductance ratio σn/σp. The dashed line marks σn/σp=1. (g) The Kohler’s plots of the MR curves at the gate voltage of −0.9 V. The non-overlapping behavior with the non-linear Hall data suggests unambiguously two-carrier transport.

the magneto-resistance (MR) at different temperatures could be rescaled by the Kohler plot. If there is a single type of charge carrier with the same scattering time at the Fermi surface (FS) everywhere, the temperature-dependent Kohler plot of the MR curve would overlap each other.40 However, there is no field range over which Kohler’s rule holds in our experiments (Figure 3g; Supplementary Figure S9). Our distinct Kohler curves strongly suggest that two types of carriers with mobilities that have different temperature dependence contribute to the entire transport.40, 41 At high magnetic fields (B4 T), the slope of Hall resistance Rxy approximately equals to 1/[e(nhne)], where nh and ne represent the hole and electron density, respectively. Positive Rxy/B at high field reveals hole-dominated transport when VG−0.9 V (Figures 3c and d). This Hall slope is sensitive to the Fermi level position, and it turns from negative to positive abruptly as VG changes from −0.6 to −0.9 V, indicating that the Fermi level moves towards the valence band (Figures 3b and c). On the contrary, at low magnetic fields (B2 T), the negative Rxx/B is attributed to the higher mobility of electrons than that of holes. Upon further decreasing VG from −0.9 to −2.2 V, the Fermi level moves away from the conduction band and the contribution to Rxy/B from electrons at low fields almost vanishes at low temperatures (Figure 3d, for example, T=2 K). This is the result of freezing the residual bulk electrons.42 Linear Rxy with positive slopes suggests a hole-dominated transport in the 50-nm-thick Cd3As2 thin film.

To quantitatively understand the Hall effect measurements, we employ the two-carrier model with following equation,40, 43

where ne (nh) and μe (μh) represent the carrier density and mobility of electrons (holes), respectively. By preforming the best fit to Equation (2), the temperature-dependent mobility and carrier density of both electrons and holes could be acquired (Supplementary Figures S7–S8). Figure 3e displays the sheet carrier density ns as a function of gate voltage, where the ambipolar transport characteristic is observed as the holes dominate the negative regime while the electrons prevail in the positive one. The hole density reaches values on the order of 1012 cm−2, comparable to the electron density under positive voltage. Remarkably, the hole mobility rises from ~500 to ~800 cm2 V−1 s−1 as the gate changes from −0.8 to −2.2 V, which is consistent with the transition from two-carrier to hole-dominant transport. In contrast, the electron mobility reaches ~3000 cm2 V−1 s−1 when the Fermi level locates in the conduction band (Supplementary Figure S3). Presumably, the hole carriers with low band velocity could suffer severe impurity scattering as observed in scanning tunneling microscopy experiments.18 So, owing to low mobility, it is difficult to observe SdH oscillations from the hole carriers. According to the equation σ=neμ, the ratio of conductivity σpn can be calculated for each gate voltage, and in general, it decreases as the temperature increases (Figure 3f), suggesting the increasing component of electron conduction in the channel. The ratio crosses 1 at about 60–100 K (dashed lines in Figure 3f), which is reasonably consistent with the previous RxxT analysis (Figure 2d). Moreover, the ratio of conductivity σp/σn exceeds 9 at 2 K for the gate voltage of −2.2 V, demonstrating the hole-dominant transport here. A detailed discussion of two-carrier transport is presented in Supplementary Section SIV (Supplementary Figures S5–S9).

Quantum oscillation serves as an effective way to probe the FS of band structure.43, 44 Under positive VG, the SdH oscillations can be well resolved as the Fermi level enters the conduction band, leading to the increase of electrons which adopt a relatively high mobility. Figure 4a shows gate-dependent SdH oscillations of Cd3As2 at 4 K. According to the linear and negative slope of Rxy/B (Figure 3a), electrons are predominant in the transport leading to the SdH oscillations at high magnetic fields. To fundamentally understand the SdH oscillations at different VG, we calculate the oscillation frequency F by taking the periodic maxima and minima of Rxx. From the equation F=(φ0/2)AF, where φ0=h/2e, we can obtain the cross-section area of the FS AF. As VG changes from 0 to 1.2 V, F increases from 18.1 to 42.5 T, translating to the variation of AF from 1.72 × 10−3 to 4.05 × 10−3 Å−2. The enlargement of FS suggests that the Fermi level moves deeper into the conduction band as VG becomes larger. According to AF=2πkF2, the Fermi vector of kF can be extracted as summarized in Table 1. In contrast, owing to the low mobility of holes, SdH oscillations were not detected under negative gate voltage when the Fermi level is near the valence band.

Figure 4
figure 4

SdH oscillations of Cd3As2 thin films. (a) Gate-dependent SdH oscillations at 4 K. The amplitude decreases as the gate voltage increases. Also, the critical magnetic field that the oscillations start shifts toward the higher field with higher gate voltage. (b) Temperature-dependent SdH oscillations at 0 V. (c) Landau level index n with respect to 1/B under different gate voltages. Integer indices denote the ΔRxx peak positions in 1/B and half integer indices represent the ΔRxx valley positions. The intercepts are close to 0.5. (d) Temperature-dependent amplitude of SdH oscillations under different gate voltages. With the best fit, the effective mass was obtained. (e) Effective mass and quantum lifetime as a function of carrier density obtained from the Hall effect measurements. The effective mass slightly increases with increasing carrier density while the quantum lifetime shows the opposite trend.

Table 1 Estimated parameters from the SdH oscillations at T=4 K

The SdH amplitude as a function of temperature can be analyzed to obtain more important parameters of the carrier transport. Here we particularly focus on the SdH oscillations under VG=0 V. The temperature-dependent amplitude ΔRxx (Figure 4b) is described by ΔRxx(T)/Rxx(0)=λ(T)/sinh(λ(T)), and the thermal factor is given by λ(T)=2kBTmcyc/(eB), where kB is the Boltzmann’s constant, is the reduced plank constant and mcyc=EF/vF2 is the cyclotron mass. By performing the best fit to the ΔRxx(T)/ΔRxx(0) equation, mcyc is extracted to be 0.029 me. Using the equation vF=kF/mcyc, we can obtain the Fermi velocity vF=9.27 × 105 m s−1 and the Fermi energy EF=143 meV. From the Dingle plot, the transport life time, τ, the mean free path l=vFτ and the cyclotron mobility μSdH=eτ/mcyc could be estimated to be 1.25 × 10−13 s, 116 nm and 7537 cm2 V−1 s−1, respectively. By performing the same analysis for other gate voltages, we can extract all the physical parameters (Figure 4e), as provided in Table 1.

As the gate voltage changes from 0 to 1.2 V, the Fermi energy increases from 143 to 254 meV after applied solid electrolyte, showing the lifting of the Fermi level into the conduction band (Table 1). Also the lifetime and Fermi velocity give remarkable values approaching ~10−13 s and 106 cm s−1, respectively, which are approximate to previous transport results of the bulk material.12, 19 With continuous electron doping by applying even larger positive VG, the Fermi level goes further into the conduction band and the amplitude of the SdH oscillations gets significantly weakened and finally vanishes, suggesting increasing scattering deep into the conduction band (Figures 4a and d; Supplementary Figure S10). To further understand the gate-tunable SdH oscillations, Berry’s phase has been evaluated from the Landau fan diagram as shown in Figure 4c. Here we assign integer indices to the ΔRxx peak positions in 1/B and half integer indices to the ΔRxx valley positions.44 According to the Lifshitz–Onsager quantization rule44: , the Berry’s phase ΦB can be extracted from the intercept, γ, in the Landau fan diagram by γ=. For nontrivial π Berry’s phase, γ should be 0 or 1, as shown in previous experiments for bulk Cd3As2.19 In our samples, under different gate voltages the intercept remains close to 0.5, indicating a trivial zero Berry’s phase. The presence of zero Berry’s phase reveals that the SdH oscillations mainly derive from the high mobility bulk conduction band. With the dimensionality reduced from bulk to thin film, Cd3As2 exhibits a transition from topological Dirac semimetal to trivial band insulator.7 The Dirac point vanishes following the band gap opening. Even so, the advantage of high mobility in the Cd3As2 bulk material is preserved along with the small effective mass and long lifetime although a large linear MR12 is absent here. The detailed magneto-transport mechanism for both the bulk and thin film of Cd3As2 remains elusive at this stage and it deserves further investigation.

Angular-dependent measurements were also employed for each gate voltage showing SdH oscillations. As the magnetic field is tilted away from the sample normal, the amplitude of the SdH oscillations starts to decrease as long as the angle passes 45° (Supplementary Section SVI, Supplementary Figure S11), presumably attributed to the anisotropic FS arising from the quantum confinement in the normal direction.7 This may explain the deviation from the bulk materials in which the SdH oscillations were observable from 0° to 90°.12 Furthermore, we use polar plots to identify the anisotropy of the MR.12 Below 1 T, the MR is nearly isotropic under different gate voltage (Figure 5a). As the magnetic field increases, the polar plots assume a dipolar pattern (Figure 5b). When increasing further the gate voltage, the dipolar component decreases, giving the trend of crossover to isotropic behavior (Figure 5c). We note that, with increasing the carrier density, it needs larger magnetic field to make the FS occupy the same Landau level. Indeed, the polar plot of 1.2 V at 9 T displays a similar pattern to that of 0 V at 5 T (Figures 5b and c), indicating the reduction of anisotropy by either lifting up EF or decreasing B. (Figure 5c). Inspired by the previous transport analysis, when the Fermi level moves into the conduction band, the anisotropy could be reduced with the enhancement of the scattering processes as evidenced by the decrease of both Hall and quantum mobility. The former one is affected by large angle scattering, that is, the transport scattering, while the latter is influenced by both small and large angle scattering (Supplementary Figure S3 and Table 1). According to the study of bulk materials,12 the anisotropy mainly originates from the anisotropic transport scattering. With increasing gate voltage, the quantum mobility decreases from ~8000 to ~2700 cm2 V−1 s−1 while the Hall mobility decrease from ~3600 to ~2500 cm2 V−1 s−1. The more rapid reduction of the quantum lifetime reduces the role of transport scattering, leading to the reduction of the anisotropy. This behavior can also be verified by the Kohler’s plots (Supplementary Section SIV).

Figure 5
figure 5

Polar plots of the angle variation of MR. (a) Polar plots of the low-field MR for selected field under different gate voltages. The MR becomes nearly isotropic below 1 T. (b) Polar plots of the high-field MR for selected field under different gate voltages. The MR pattern changes from an isotropic to a dipolar form with increasing magnetic field, suggesting the anisotropy of MR under high field. (c) Polar plots of the MR fixed at selected field under different gate voltages. Under larger gate voltage, the EF becomes large and the anisotropy is reduced.


In conclusion, taking advantage of the high capacitance of the solid electrolyte, we demonstrate for the first time a gate-tunable transition of band conduction to hopping conduction in single-crystalline Cd3As2 thin films grown by molecular beam epitaxy. The two-carrier transport along with the controllable RxxT suggests that Cd3As2 can generate a small band gap as the system reduces dimensionality. Importantly, SdH oscillations emerge when the Fermi level enters into the conduction band with high electron mobility. Thus, Cd3As2 thin film systems hold promise for realizing ambipolar field effect transistors and for observing intriguing quantum spin Hall effect.