Gate-tunable quantum oscillations in ambipolar Cd3As2 thin films

Electrostatic doping in materials can lead to various exciting electronic properties, such as metal-insulator transition and superconductivity, by altering the Fermi level position or introducing exotic phases. Cd3As2, a three-dimensional (3D) analog of graphene with extraordinary carrier mobility, was predicted to be a 3D Dirac semimetal, a feature confirmed by recent experiments. However, most research so far has been focused on metallic bulk materials that are known to possess ultra-high mobility and giant magnetoresistance but limited carrier transport tunability. Here, we report on the first observation of a gate-induced transition from band conduction to hopping conduction in single-crystalline Cd3As2 thin films via electrostatic doping by solid electrolyte gating. The extreme charge doping enables the unexpected observation of p-type conductivity in a 50 nm-thick Cd3As2 thin film grown by molecular beam epitaxy. More importantly, the gate-tunable Shubnikov-de Haas (SdH) oscillations and the temperature-dependent resistance reveal a unique band structure and bandgap opening when the dimensionality of Cd3As2 is reduced. This is also confirmed by our first-principles calculations. The present results offer new insights towards nanoelectronic and optoelectronic applications of Dirac semimetals in general, and provide new routes in the search for the intriguing quantum spin Hall effect in low-dimension Dirac semimetals, an effect that is theoretically predicted but not yet experimentally realized.


INTRODUCTION
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 , Na3Bi 6 and Cd3As2 7 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 (TIs) 7,8 , axion and band insulators 6,8-10 , 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 due 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 TI phase may eventually emerge upon the breaking of crystal symetry 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 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 plays a vital role for the study of the transport behavior and TDSs-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-doublelayer transistor (EDLT) 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 letter, 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 (MBE) (see Method). 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 10 13 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 425B molecular beam epitaxy system. Cd3As2 bulk material (99.9999%, American Elements Inc.) 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 Cd 3 As 2 . The crystal structure was determined by X-ray Diffraction (XRD, Bruker D8 Discovery) and high-resolution Transmission Electron Microscopy (HRTEM, JEOL 2100F, 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) and poly (ethylene oxide) (PEO, Mw=100,000, Sigma Aldrich) powers were mixed with anhydrous methanol (Alfa Aesar). 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) and Agilent 2912 source meters was used to acquire experimental data.
Band structure calculations. Density functional theory based first-principles calculations were performed for bulk Cd3As2. The resulting bulk Hamiltonian was projected onto a basis of Cd 5s and As 4p states, using wannierfunctions 35  has been shown to crystallize into the I41/acd space group (which is a√2 √2 2 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 (VASP) 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 To carry out low-temperature transport measurements, a ~50 nm-thick Cd3As2thin film was patterned into a standard Hall bar configuration with a channel dimension of 2mm × 1mm. 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 over 24.9 meV from Ea, which is reasonable for the Cd3As2 thin film of this thickness. The sheet carrier density, ns, at 2K is determined to be 1.5 × 10 12 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.
With ionic gating, we can efficiently tune the Fermi level in order to achieve twocarrier transport in Cd3As2. Several as-grown Cd3As2 thin films have been measured 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 (VG≥0.5 V, Fig. 2c). However, when VG becomes negative, Rxx shows a completely negative temperature dependence without metallic behavior owing to the insufficient hole doping (Fig. 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 Rxx-T 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 larger than 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 VIII). This variation in the bulk gap is in reasonable agreement with our experimental results.
In order to further study the gate-tunable Rxx-T 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 Fig. 3a-d). According to the Kohler's rule [38][39][40]  VG≤-0.9 V (Fig. 3c-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 ( Fig. 3b-c). On the contrary, at low magnetic fields (B≤2T), 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. 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. 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 10 12 cm -2 , comparable to the electron density under positive voltage. Remarkably, the hole mobility rises from ~500 to ~800 cm 2 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 cm 2 V -1 s -1 when the Fermi level locates in the conduction band ( Supplementary Fig. 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 the low mobility, it is difficult to observe the SdH oscillations from the hole carriers. According to the equation σ=neμ, the ratio of conductivity σp/σn can be calculated for each gate voltage, and in general it decreases as the temperature increases (Fig. 3f), suggesting the increasing component of electron conduction in the channel. The ratio crosses 1 at about 60~100 K (dashed lines in Fig.   3f), which is reasonably consistent with the previous Rxx-T analysis (Fig. 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 IV.
Quantum oscillation serves as an effective way to probe the Fermi surface 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 (Fig. 3a)  and 7537 cm 2 V -1 s -1 , respectively. By performing the same analysis for other gate voltages, we can extract all the physical parameters (Fig. 4e), as provided in Table I.
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 I). Also the lifetime and Fermi velocity give remarkable values approaching ~10 -13 s and 10 6 cm/s, respectively, which are approximate to previous transport results of the bulk material 12,19 . 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 VI), presumably attributed to the anisotropic Fermi surface 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°1 2 . 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 (Fig. 5a). As the magnetic field increases, the polar plots assume a dipolar pattern (Fig. 5b). When increasing further the gate voltage, the dipolar component decreases, giving the trend of crossover to isotropic behavior (Fig. 5c). We note that with increasing the carrier density, it needs larger magnetic field to make the Fermi surface 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 (Fig. 5b-c), indicating the reduction of anisotropy by either lifting up EF or decreasing B. (Fig. 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, i.e., the transport scattering, while the latter is influenced by both small and large angle scattering ( Supplementary Fig. S3 and Table I). 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 cm 2 V -1 s -1 while the Hall mobility decrease from ~3600 to 2500 cm 2 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 IV).

CONCLUSION
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 MBE. The two-carrier transport along with the controllable Rxx-T 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.

CONFLICT OF INTEREST
The authors declare no conflict of interest.      Yanwen Liu et al. Table 1