Abstract
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. Cd_{3}As_{2}, a threedimensional (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 ultrahigh mobility and giant magnetoresistance but limited carrier transport tunability. Here we report on the first observation of a gateinduced transition from band conduction to hopping conduction in singlecrystalline Cd_{3}As_{2} thin films via electrostatic doping by solid electrolyte gating. The extreme charge doping enables the unexpected observation of ptype conductivity in a ∼50nmthick Cd_{3}As_{2} thin film grown by molecular beam epitaxy. More importantly, the gatetunable Shubnikov–de Haas oscillations and the temperaturedependent resistance reveal a unique band structure and bandgap opening when the dimensionality of Cd_{3}As_{2} is reduced. This is also confirmed by our firstprinciple calculations. The present results offer new insights toward nanoelectronic and optoelectronic applications of Dirac semimetals in general and provide new routes in the search for the intriguing quantum spin Hall effect in lowdimension 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 twodimensional (2D) Dirac fermions with linear energy dispersion.^{1, 2, 3, 4} Recently, the existence of threedimensional (3D) Dirac fermions has been theoretically predicted while several potential candidates, including βBiO_{2},^{5} Na_{3}Bi^{6} and Cd_{3}As_{2}^{7} were explored as topological Dirac semimetals (TDSs), in which the Dirac nodes are developed via the point contact of conductionvalence 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, Cd_{3}As_{2} 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 Cd_{3}As_{2} have been widely investigated, hampered by the complicated crystal structure its band structure remains a matter of controversy.^{14, 15} Recently, firstprinciple calculations have revealed the nature of 3D topological Dirac semimetal state in Cd_{3}As_{2}.^{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 Cd_{3}As_{2}, a theoretically predicted topological insulator phase may eventually emerge upon the breaking of crystal symmetry.^{7} Furthermore, thicknessdependent quantum oscillations could be anticipated to arise from arclike surface states.^{20} Such perspective manifests the superiority of Cd_{3}As_{2} 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 Cd_{3}As_{2} 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 Cd_{3}As_{2} always exhibits ntype conductivity with a high electron concentration, therefore calling for a wellcontrolled 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, E_{F}, is close to the Dirac nodes.^{28} Hence, the ability to modulate the carrier density and E_{F} in Cd_{3}As_{2} has a vital role for the study of the transport behavior and TDSrelated phase transitions. In view of preserving high mobility in Cd_{3}As_{2}, the electrostatic doping is an advantageous choice owing to its tunable and defectfree nature compared with the chemical doping.
To modulate a largearea flat film on an insulating substrate, an electricdoublelayer 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 waferscale Cd_{3}As_{2} thin films, deposited on mica substrates by molecular beam epitaxy (see Material and methods). Our transport measurements reveal a semiconductorlike temperaturedependent 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, n_{s}, 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 holedominated twocarrier transport is achieved by applying negative gate voltage, a strong indication of ambipolar effect, thus demonstrating the great potential of Cd_{3}As_{2} thin films in electronic and optical applications.
Materials and methods
Sample growth
Cd_{3}As_{2} thin films were grown in a Perkin Elmer (Waltham, MA, USA) 425B molecular beam epitaxy system. Cd_{3}As_{2} bulk material (99.9999%, American Elements Inc., Los Angeles, CA, USA) was directly evaporated onto 2inch 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 highenergy electron diffraction (RHEED) system.
Characterizations of crystal structure of Cd_{3}As_{2}
The crystal structure was determined by Xray diffraction (Bruker D8 Discovery, Bruker Inc., Billerica, MA, USA) and highresolution 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: LiClO_{4} (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 magnetotransport measurements were performed in a Physical Property Measurement System by Quantum Design with a magnetic field up to 9 T. A homemade measurement system, including lockin 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 theorybased firstprinciple calculations were performed for bulk Cd_{3}As_{2}. 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 abinitioderived tightbinding 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, Cd_{3}As_{2} 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 Cd_{3}As_{2} was used to perform the simulations. Density functional theory computations were performed using Vienna Abinitio Simulation Package,^{36} including spinorbit coupling. The Perdew–Burke–Ernzerhof parameterization to the exchangecorrelation functional was used.^{37} A plane wave cutoff of 600 eV was employed, along with a 6 × 6 × 3 Monkhorst–Pack kgrid.
Results and discussion
TEM was carried out to characterize the crystal structure of Cd_{3}As_{2}. A typical selectedarea 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 asgrown 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 Xray diffraction (Figure 1d), which further confirms the TEM observations.
To carry out lowtemperature transport measurements, a ~50nmthick Cd_{3}As_{2} thin film was patterned into a standard Hall bar configuration with a channel dimension of 2 × 1 mm^{2}. 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 temperaturedependent resistance R_{xx} of the pristine Cd_{3}As_{2} thin film prior to the ionic gating process. The negative dR_{xx}/dT suggests semiconducting behavior that is different from the metallic nature of the bulk counterpart.^{12, 19} The activation energy (E_{a}) is extracted to be 12.45 meV by fitting the Arrhenius plot of R_{xx} at high temperature (from 280 to 350 K) with the equation R_{xx}~exp(E_{a}/k_{B}T), where k_{B} is the Boltzmann constant and T is the measurement temperature. The band gap, E_{gap}, is roughly estimated to be >24.9 meV from E_{a}, which is reasonable for the Cd_{3}As_{2} thin film of this thickness. The sheet carrier density, n_{s}, at 2 K 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 Cd_{3}As_{2} thin films.
With ionic gating, we can efficiently tune the Fermi level in order to achieve twocarrier transport in Cd_{3}As_{2}. Several asgrown Cd_{3}As_{2} 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<V_{G}<0.5 V, Figure 2c), R_{xx} shows a negative temperature dependence, indicative of a semiconducting state. Increasing V_{G} up to 1.2 V, a metallic behavior is witnessed by a change of negative to positivetemperature dependence. This behavior originates from the fact that the Fermi level has been moved into the conduction band (V_{G}⩾0.5 V, Figure 2c). However, when V_{G} becomes negative, R_{xx} shows a completely negativetemperature 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 R_{xx}–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 holedominated transport at low temperatures, which will be investigated in the following section on magnetotransport. The bandgap opening behavior here shows a good agreement with our firstprinciple calculations. Figure 2e displays the calculated band structure of a typical Cd_{3}As_{2} 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 gatetunable R_{xx}–T behavior and ascertain the carrier type, magnetotransport measurements were carried out at low temperatures. A clear Hall anomaly at different V_{G} was observed (see Figures 3a–d). According to the Kohler’s rule,^{38, 39, 40}
the magnetoresistance (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 temperaturedependent 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 (B⩾4 T), the slope of Hall resistance R_{xy} approximately equals to 1/[e(n_{h}−n_{e})], where n_{h} and n_{e} represent the hole and electron density, respectively. Positive R_{xy}/B at high field reveals holedominated transport when V_{G}⩽−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 V_{G} 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 (B⩽2 T), the negative R_{xx}/B is attributed to the higher mobility of electrons than that of holes. Upon further decreasing V_{G} from −0.9 to −2.2 V, the Fermi level moves away from the conduction band and the contribution to R_{xy}/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 R_{xy} with positive slopes suggests a holedominated transport in the ∼50nmthick Cd_{3}As_{2} thin film.
To quantitatively understand the Hall effect measurements, we employ the twocarrier model with following equation,^{40, 43}
where n_{e} (n_{h}) and μ_{e} (μ_{h}) represent the carrier density and mobility of electrons (holes), respectively. By preforming the best fit to Equation (2), the temperaturedependent mobility and carrier density of both electrons and holes could be acquired (Supplementary Figures S7–S8). Figure 3e displays the sheet carrier density n_{s} 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 twocarrier to holedominant transport. In contrast, the electron mobility reaches ~3000 cm^{2} 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 σ_{p}/σ_{n} 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 R_{xx}–T analysis (Figure 2d). Moreover, the ratio of conductivity σ_{p}/σ_{n} exceeds 9 at 2 K for the gate voltage of −2.2 V, demonstrating the holedominant transport here. A detailed discussion of twocarrier 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 V_{G}, 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 gatedependent SdH oscillations of Cd_{3}As_{2} at 4 K. According to the linear and negative slope of R_{xy}/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 V_{G}, we calculate the oscillation frequency F by taking the periodic maxima and minima of R_{xx}. From the equation F=(φ_{0}/2π^{2})A_{F}, where φ_{0}=h/2e, we can obtain the crosssection area of the FS A_{F}. As V_{G} changes from 0 to 1.2 V, F increases from 18.1 to 42.5 T, translating to the variation of A_{F} 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 V_{G} becomes larger. According to A_{F}=2πk_{F}^{2}, the Fermi vector of k_{F} 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.
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 V_{G}=0 V. The temperaturedependent amplitude ΔR_{xx} (Figure 4b) is described by ΔR_{xx}(T)/R_{xx}(0)=λ(T)/sinh(λ(T)), and the thermal factor is given by λ(T)=2π^{2}k_{B}Tm_{cyc}/(ℏeB), where k_{B} is the Boltzmann’s constant, ℏ is the reduced plank constant and m_{cyc}=E_{F}/v_{F}^{2} is the cyclotron mass. By performing the best fit to the ΔR_{xx}(T)/ΔR_{xx}(0) equation, m_{cyc} is extracted to be 0.029 m_{e}. Using the equation v_{F}=ℏk_{F}/m_{cyc}, we can obtain the Fermi velocity v_{F}=9.27 × 10^{5} m s^{−1} and the Fermi energy E_{F}=143 meV. From the Dingle plot, the transport life time, τ, the mean free path l=v_{F}τ and the cyclotron mobility μ_{SdH}=eτ/m_{cyc} could be estimated to be 1.25 × 10^{−13} s, 116 nm 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 (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 10^{6} 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 V_{G}, 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 gatetunable 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 ΔR_{xx} peak positions in 1/B and half integer indices to the ΔR_{xx} valley positions.^{44} According to the Lifshitz–Onsager quantization rule^{44}: , the Berry’s phase Φ_{B} 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 Cd_{3}As_{2}.^{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, Cd_{3}As_{2} 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 Cd_{3}As_{2} bulk material is preserved along with the small effective mass and long lifetime although a large linear MR^{12} is absent here. The detailed magnetotransport mechanism for both the bulk and thin film of Cd_{3}As_{2} remains elusive at this stage and it deserves further investigation.
Angulardependent 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 E_{F} 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 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 SIV).
Conclusion
In conclusion, taking advantage of the high capacitance of the solid electrolyte, we demonstrate for the first time a gatetunable transition of band conduction to hopping conduction in singlecrystalline Cd_{3}As_{2} thin films grown by molecular beam epitaxy. The twocarrier transport along with the controllable R_{xx}–T suggests that Cd_{3}As_{2} 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, Cd_{3}As_{2} thin film systems hold promise for realizing ambipolar field effect transistors and for observing intriguing quantum spin Hall effect.
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Acknowledgements
This work was supported by the National Young 1000 Talent Plan, Pujiang Talent Plan in Shanghai, Ministry of Science and Technology of China (973 Project Nos.2013CB923901) and National Natural Science Foundation of China (61322407, 11474058, 61474061, 11274066, U1330118). Part of the sample fabrication was performed at Fudan Nanofabrication Laboratory. We thank Mr Yijun Yu and Professor Yuanbo Zhang for great assistance on solid electrolyte. We thank Professor Shiyan Li for the inspiring discussions. AN acknowledges support from the Irish Research Council under the EMBARK initiative. SS acknowledges support from the European Research Council (QUEST project).
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Liu, Y., Zhang, C., Yuan, X. et al. Gatetunable quantum oscillations in ambipolar Cd_{3}As_{2} thin films. NPG Asia Mater 7, e221 (2015). https://doi.org/10.1038/am.2015.110
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DOI: https://doi.org/10.1038/am.2015.110
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