# Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium

^{a}International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China;^{b}Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China;^{c}Chinese Academy of Sciences Key Laboratory of Strongly Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China;^{d}National Synchrotron Radiation Laboratory, University of Science and Technology of China, 230029 Hefei, Anhui, China;^{e}Department of Physics, Southern University of Science and Technology, 518055 Shenzhen, China;^{f}Institutes of Physical Science and Information Technology, Anhui University, 230601 Hefei, Anhui, China;^{g}High Magnetic Field Laboratory, Chinese Academy of Sciences, 230031 Hefei, Anhui, China;^{h}Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, 430074 Wuhan, China

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Edited by Junichiro Kono, Rice University, Houston, TX, and accepted by Editorial Board Member Angel Rubio April 4, 2020 (received for review February 15, 2020)

## Significance

Recent intensive investigations have revealed unique electronic transport properties in solids hosting Weyl fermions, which were originally proposed in high-energy physics. Up to now, the discovered Weyl systems have been limited to semimetal compounds. Here we demonstrate that the elemental semiconductor tellurium is a Weyl semiconductor, with typical Weyl signatures, including the negative longitudinal magnetoresistance, the planar Hall effect, as well as the intriguing logarithmically periodic magneto-oscillations in the quantum limit regime. Such Weyl semiconductors offer a simple platform for the exploration of novel Weyl physics and topological device applications based on semiconductors and moreover confirm the universality of discrete scale invariance in topological materials.

## Abstract

The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe_{5} and HfTe_{5}. The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop “Weyl semiconductors” provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.

- Weyl semiconductor
- tellurium
- negative longitudinal magnetoresistance
- planar Hall effect
- log-periodic oscillations

The discovery of nontrivial topological phases has reshaped our understanding of solid-state materials (1⇓–3). Besides band structure measurements, transport properties can also provide some unique signatures to identify these exotic topological phases. For example, two well-known transport signatures in Dirac/Weyl semimetals are the chiral-anomaly induced negative longitudinal magnetoresistance (NLMR) (4⇓⇓⇓⇓⇓⇓⇓⇓⇓–14) and planar Hall effect (PHE) (12, 15⇓⇓⇓⇓–20). Recently, a new type of quantum oscillations featuring log-periodicity, wherein the extrema magnetic fields of oscillations constitute a geometric series, was discovered in ZrTe_{5} (21) and HfTe_{5} (22) beyond the quantum limit. Physically, these unusual log-periodic oscillations can be attributed to the manifestation of discrete scale invariance (DSI) (21, 23, 24), whereby self-reproduction occurs at specific scales that form a geometric series. The DSI character of topological materials is rooted in the two-body quasi-bound states formed between linearly dispersed quasi-particles and opposite charge centers, with the energy levels satisfying a geometric progression (21). In theory, log-periodic oscillations are considered a universal feature of materials hosting Dirac/Weyl fermions with Coulomb attraction (21, 23, 24).

Until now, Dirac/Weyl physics has been generally regarded as unique to semimetals, with the Dirac/Weyl points located around the Fermi level. Nevertheless, considering the high tunability and compatibility with modern electronic industry, the semiconductor will be a better candidate material for designing topological electronic devices if exotic transport phenomena related to Dirac/Weyl fermions can be realized. Tellurium (Te) is a narrow band-gap semiconductor possessing strong spin–orbit coupling, and it lacks space inversion symmetry due to the characteristic chiral crystal structure. As an elemental semiconducting material, Te has been widely studied for its lattice dynamics, band structure, transport, and optical properties, with key discoveries transpiring several decades ago (25). Recently, the Weyl semimetal phase was theoretically proposed in Te by closing its bulk band gap with external perturbations (26, 27), which has renewed interest in exploring the possible topological characters of Te (26, 28⇓–30).

In this work, we report two transport signatures (NLMR and PHE) to reveal Weyl-related topological properties in the self-hole-doped elemental semiconductor Te. The Weyl band characteristic further manifests as the logarithmically periodic magneto-oscillations in the quantum limit regime. Our results demonstrate that these “Weyl semiconductors” (semiconductors hosting Weyl fermions, as schematically shown in Fig. 1*A*) can serve as a simple and ideal platform for the exploration of Weyl physics and devices beyond conventional semimetal materials.

## Results

### Electronic Band Structure of Te.

The chiral structure of Te with no inversion symmetry is shown in Fig. 1*B*. The first-principles band structure of Te is shown in *SI Appendix*, Fig. S2 (see *Materials and Methods* for calculation details), which demonstrates that Te is a narrow-gap semiconductor exhibiting strong spin–orbit coupling. Its band gap (∼0.38 eV) is near the corner of the Brillouin zone, that is, the H point (Fig. 1*B*), which is consistent with previous results (26, 31). Along the high symmetric H–L line, two Weyl points arise from the crossing of two spin-splitting valence bands, as shown in Fig. 1*C*. They are located below the Fermi level by −0.20 eV (designated W_{1}) and −0.36 eV (designated W_{2}), respectively. The calculated band structure exhibits good overall agreement with our angle-resolved photoemission spectroscopy measurements (*SI Appendix*, Fig. S3*A* and *Note 2*), although the two Weyl points cannot be seen clearly due to limited spectroscopy resolution.

Te single crystals were grown via physical vapor deposition (*Materials and Methods*). The as-grown crystals are normally hole-doped and possess a typical carrier density on the order of 10^{16} cm^{−3}, consistent with previous reports in which samples were grown using a similar method (30, 32). The hole-doped character is further verified via the angle-resolved photoemission spectroscopy results (*SI Appendix*, Fig. S3*B* and *Note 2*). Since there are no detectable impurities in our Te crystals, such self-hole-doping characteristics may result from Te vacancies which act as acceptors (33). Our first-principles calculation further demonstrates that the presence of vacancies indeed prompts the Fermi level to shift toward the valence bands (*SI Appendix*, Fig. S4). Below we will present the comprehensive magnetotransport measurement results for a typical Te single-crystal sample, in which signatures of Weyl-related physics are clearly observed.

### NLMR Effect.

Fig. 2*A* shows the temperature (*T*)-dependent resistance (*R*) curve of sample 6, which exhibits typical behaviors of a doped semiconductor (as detailed in *SI Appendix*, *Note 3*). Fig. 2 *B* and *C* show the curves for the magnetoresistance [MR, defined as *SI Appendix*, Fig. S5 and discussed in *SI Appendix*, *Note 4*. For the perpendicular case (*B*⊥*I*), the MR is positive and exhibits clear linear behavior (Fig. 2*B*). In contrast, markedly negative MR behavior is demonstrated for *B*∥*I* (Fig. 2*C*). At *T* = 25 K, the negative MR achieves a magnitude up to ∼22% at 14 T, which is comparable to the NLMR effect reported for several Weyl semimetals such as WTe_{2} (11) and Co_{3}Sn_{2}S_{2} (7). The negative MR degrades accordingly with increasing temperature due to the thermal effect but remains observable up to ∼100 K.

The occurrence of NLMR in the presence of parallel magnetic and electric fields serves as an important signature of the chiral anomaly (13, 34) in material systems hosting Weyl fermions (4, 6⇓⇓⇓⇓⇓–12, 14). Theoretically, the longitudinal magnetoconductivity can be described using the following equation (8):*D*, *Inset* (*SI Appendix*, Fig. S8*A*), the experimental data can be well-fitted via Eq. **1**, and the extracted *D*). The chiral coefficient

To gain further insight into the observed negative MR, we also studied its angular-dependent character. Fig. 2*E* shows the MR for different angles *B* with respect to *I* as measured at 25 K. Rotating the magnetic field away from *B*⊥*I* prompts the positive MR magnitude to decrease accordingly. Signatures of negative MR occur for *B*∥*I*). In addition, the ^{2}*θ* (Fig. 2*F* and *SI Appendix*, Fig. S8*B*), which is consistent with observations in topological semimetals (12). Similar angular-dependent MR behavior is observed at temperatures down to 2 K, although the negative MR is largely outweighed by the enormous positive MR background attributed to magnetic freeze-out (35) (*SI Appendix*, Fig. S9).

Thus far, the negative MR observed in Te crystals under *B*∥*I* could be well explained via the chiral anomaly, reproducing previous observations of Weyl semimetals (for data from additional samples see *SI Appendix*, Figs. S10 and S11). Other possible origins, such as weak localization and current jetting, were examined carefully and eventually ruled out (*SI Appendix*, *Note 6*).

### PHE.

The PHE, which manifests as the appearance of in-plane transverse voltage when the in-plane magnetic field is not exactly parallel or perpendicular to the current, is another important transport signature of Weyl physics (19, 20). The configuration for measuring the PHE is depicted in Fig. 3*A*, *Inset*. Even though a conventional Hall component may still exist in such a setup due to misalignment between the actual rotation plane and the sample plane, it can be eliminated by simply averaging the Hall resistances measured under positive and negative magnetic fields. Fig. 3*A* shows the symmetrized planar Hall resistivity *SI Appendix*, Fig. S13*A*. Both the planar Hall resistivity and the in-plane AMR display a 180° periodic angular dependence, with the AMR reaching its maximum and minimum at 90° and 0°, respectively, while

Theoretically, PHE arising from the chiral anomaly could be fitted via the following equation (17) (*SI Appendix*, *Note 7*):*A* shows that Eq. **2** provides an excellent fit for the experimental *C* clearly demonstrates that the obtained *B* < 3 T, *B*^{2}. In the relatively high field regime (*B* > 4.5 T), *B* and displays no evidence of saturation up to *B* = 14 T. Similar field dependence has been previously reported for the PHE in topological semimetals (17, 18).

Fig. 3*B* shows the temperature-dependent PHE behavior (see *SI Appendix*, Fig. S13*B* for the AMR data taken simultaneously). With increasing temperature, the extracted *T* ∼ 100 K (Fig. 3*D*). Such behavior is remarkably consistent with that of the *D*, suggesting the same underlying physical origin of both the PHE and NLMR in the present Te crystals (see *SI Appendix*, *Note 4* for further discussion).

The above-discussed experimental observations of the NLMR and PHE in Te crystals adhere well to the chiral-anomaly mechanism in materials possessing Weyl fermions. On the other hand, it has been theoretically proposed that both the NLMR and PHE can be observed in a system with nonzero Berry curvature at the Fermi level (36, 37). One notices that the nonzero Berry curvature is also induced by either inversion or time-reversal symmetry breaking, which is the same to the realization of Weyl fermions (3, 38). Therefore, both mechanisms originate from symmetry breaking. To explore the band topology of Te, the Berry curvature (Ω) of the highest occupied valence band is calculated. The Fermi level (E_{F}) is set at ∼2 meV below the valence band maximum according to the typical carrier densities of samples at 25 K (*SI Appendix*, Fig. S14*A*). Nonzero Berry curvature on the Fermi surface, shown in Fig. 1*D*, is dominated by the contribution of the Weyl point W_{1} (see *SI Appendix*, Fig. S14*B* and *Note 8*). This gives a strong evidence of correlation between the observed NLMR and Weyl physics. Recent theoretical works have predicted that Te can be turned into a Weyl semimetal via closing the band gap by applying high pressure (26, 27). In contrast, here we reveal that the pristine semiconductor Te can be considered a “Weyl semiconductor,” since Weyl fermions and related exotic transport properties can be directly realized without gap closing.

### Log-Periodic MR/Hall Oscillations.

Unusual properties of material systems under the quantum limit, wherein all of the carriers are condensed to the lowest Landau level, have been a topic of interest since their discovery (21, 22, 39⇓⇓⇓⇓–44). As a promising candidate for “Weyl semiconductor” with a relatively small carrier density and unique band topology, Te offers a suitable platform for the study of Weyl physics beyond the quantum limit. For the studied Te sample 6 with carrier density of ∼3.9 × 10^{16} cm^{−3} at 2 K, the estimated critical field *SI Appendix*, *Note 9*), which is readily achievable. In fact, the MR curves for *B*⊥*I* obtained in the low temperature range of 2 to 10 K (*SI Appendix*, Fig. S5*B*) exhibit an oscillatory character even above

To reveal the feature of these unexpected magneto-oscillations, we conducted magnetotransport measurements of sample 6 in two high-magnetic-field facilities (*Materials and Methods*). Fig. 4*A* shows the MR data taken under static fields at 1.8 K, which exhibit oscillations with more periods. Following previous studies (21, 22), a suitable background (*SI Appendix*, Fig. S15*A*) obtained via smoothing was subtracted to better distinguish the oscillations (*Materials and Methods*). The results are presented in Fig. 4*A*, *Bottom* with dashed vertical lines marking the positions of peaks/dips. Interestingly, the interval between adjacent dashed lines grows larger as the magnetic field increases. For better presentation, the extrema fields (*B*_{n}) corresponding to these peaks/dips were extracted, and 1/*B*_{n} and log(*B*_{n}) were plotted as a function of the extrema index (*n*), respectively (Fig. 4*C*). Here the peaks and dips are assigned to integers and half-integers, respectively. The clear deviation from the linear dependence of 1/*B*_{n} on *n* further demonstrates the inability of the Shubnikov–de Haas effect to account for the observed oscillations. In contrast, the well-defined linear behavior observed for the log(*B*_{n}) vs. *n* curve indicates the log-periodicity. Note that the point at ∼3.1 T deviates from the linear trend, possibly because this field is below the quantum limit, or perhaps as a result of some unavoidable anomalies during the background subtraction (*SI Appendix*, *Note 9*). Fig. 4*B* shows the MR data taken across a wider field range at 2.5 K using pulsed fields. These data exhibit more oscillations than do the data shown in Fig. 4*A*, while both the low field data and the extracted *B*_{n} are consistent across both datasets (see also Fig. 4*C*).

Fig. 4*D* presents the Hall data obtained simultaneously with the MR data from Fig. 4*A*. The log-periodic character is also evident from a comparison of the index dependence of the 1/*B*_{n} and log(*B*_{n}) curves (Fig. 4*E*). The fast Fourier transform for log(*ΔR*_{xx}) and log(*ΔR*_{xy}) shows nearly identical periods, indicating the same origin for both the observed MR and Hall oscillations.

As aforementioned, the oscillations with peculiar log-periodicity have been experimentally observed only recently, and only in ZrTe_{5} (21) and its sister compound HfTe_{5} (22). The phenomenon is regarded as the manifestation of DSI in solid-state systems and is theoretically considered to be universal in topological materials hosting Dirac/Weyl fermions with Coulomb attraction (21⇓⇓–24). The underlying mechanism can be summarized as follows (21, 24): Dirac/Weyl fermions in an attractive Coulomb potential possess a continuous scaling symmetry. In the supercritical case *e* is the elementary charge, *ε*_{0} is the vacuum permittivity, *ћ* is the reduced Planck constant, and

Here we would like to attribute the observed log-periodic oscillations in Te crystals to the DSI after excluding another possible origin (*SI Appendix*, *Note 9*). The quasi-bound states are likely formed between Weyl fermions located near the top of valence bands and opposite charge centers. Since the self-hole-doping characteristic may result from Te vacancies acting as acceptors (33), such vacancies are likely to serve as the negative charge centers that exert Coulomb attraction on the positive Weyl fermions (see *SI Appendix*, Fig. S4 for the calculation results).

For the log-periodic oscillations, the scale factor (*λ*) for the DSI can be defined as *B*_{n}/*B*_{n+1}. As such, this quantity is estimated to be ∼2.33 for sample 6, as based on linear fitting of the log(*B*_{n}) vs. *n* plot (Fig. 4*C*). This value of *λ* is consistent with that obtained from the fast Fourier transform analysis, which is ∼2.10 (∼2.28) for the MR (Hall) oscillations (Fig. 4*F*). In ref. 21, the semiclassical quantization condition leads to the DSI with *Z* = 1 and the lowest angular momentum channel with *κ =* ±1 (21). Thus, the fine-structure constant (*α*) is calculated to be ∼7.5, far exceeding 1/137 due to the small Fermi velocity of Te crystals. According to ^{5} m/s, which is comparable to the value (∼1.9 × 10^{5} m/s) estimated from the calculated band structure. The small

With increasing temperature, the amplitudes for both the MR and Hall oscillations decline accordingly before becoming indiscernible at temperatures above 15 K (*SI Appendix*, Fig. S16 and *Note 10*). Similar behaviors are also observed in other samples (*SI Appendix*, Fig. S17). This can be attributed to the thermionic excitation that weakens the Coulomb attraction. However, compared to the cases of ZrTe_{5} and HfTe_{5}, the critical temperature above which the oscillations disappear is much smaller for the present Te crystals, implying the relatively small binding energy of the as-formed quasi-bound states (as discussed in *SI Appendix*, *Note 10*).

## Conclusion

The present work clearly demonstrates the realization of Weyl-related properties in a narrow-gap semiconductor with strong spin–orbit coupling and without inversion symmetry, thus greatly broadening the scope of topological materials. Furthermore, the highly tunable electronic performance of Weyl semiconductors enables further manipulation of Weyl fermions through various means commonly adopted in semiconductor electronics, such as electrostatic gating and optical illumination. Moreover, the observation of the log-periodic magneto-oscillations further confirms the universality of DSI in topological materials hosting Dirac/Weyl fermions with Coulomb attraction, thus endowing Te with a novel platform for the study of intriguing ground states beyond the quantum limit. The successful introduction of Weyl physics into semiconductor systems therefore offers a new dimension for the future design of topological semiconductor devices.

## Materials and Methods

### Growth of Te Single Crystals.

High-quality Te single crystals were grown using a physical vapor transport technique. High-purity (99.999% pure) Te powder was loaded into a quartz tube, and a small amount of C powder was added to remove trace oxygen. The quartz tube was heated to 1,000 °C over the course of 5 h and subsequently maintained at 1,000 °C for 1 h. Then, the tube was cooled at a rate of 20 °C/h to 400 °C and 300 °C for the hot and the cold zone, respectively. After maintaining the set temperature for 2 wk, the tube was slowly cooled to room temperature, and rod-like silvery crystals (typical dimensions 5 × 0.3 × 0.1 mm^{3}) were obtained (Fig. 2*A*, *Inset*).

### Structure and Composition Characterization.

The structure of Te single crystals was measured by a Rigaku SmartLab X-ray diffractometer (XRD) at room temperature using monochromatic Cu-Kα radiation (λ = 1.5418 Å). A typical XRD spectrum is shown in *SI Appendix*, Fig. S1*A*. In the wide range spectrum, only the sharp peaks from the Te *θ* range, such that the detection of many lattice planes is possible without breaking the single crystal. As also shown in *SI Appendix*, Fig. S1*A*, the measured data match well with the standard powder XRD pattern of Te. *SI Appendix*, Fig. S1*B* shows the high-resolution scanning transmission electron microscopy (Thermo Fisher Themis G2 60-300) imaging and selective area electron diffraction pattern of the exposed surface, which both further demonstrate the high quality of the single crystal at the atomic scale. The crystalline long axis, that is, the growth direction, is the [0001] direction. The lattice parameters were determined to be a = b = 4.48 Å, c = 6.00 Å. The chemical composition of the crystals was examined by an energy dispersive spectrometer (INCA detector; Oxford Instruments) attached to a field-emission scanning electron microscope (Sirion 200; FEI) operated at 20 kV. No impurity elements were detected (*SI Appendix*, Fig. S1*C*).

### Magnetic and Transport Property Measurements.

The magnetic properties were analyzed using a Quantum Design SQUID-VSM system with the magnetic field up to 7 T and the temperature down to 2 K. For electrical transport measurements, electron beam lithography was utilized to define the electrode pattern on the surface of the Te crystals, then 10 nm Pd and 50 nm Au were deposited as electrode materials using the e-beam evaporation method. Silver epoxy was subsequently used to affix the wires to the Pd/Au contacts. The measurements were performed in a Quantum Design Physical Property Measurement System with the magnetic field up to 14 T. The planar Hall measurements were performed via rotating the sample in a fixed magnetic field. The angle of 105° is the starting point for the measurement, and the mechanical backlash of the rotator normally leads to slight discontinuity at an angle of around 105° in the planar Hall data. High-field transport measurements were carried out in the High Magnetic Field Laboratory in Hefei (static field, 33 T) and the Wuhan National High Magnetic Field Center (pulsed field, 53 T). Due to the rod-like shape of Te crystals (Fig. 1*F*, *Inset*), the current was applied along the long axis (the [0001] direction) during all transport measurements conducted in this study.

### Angle-Resolved Photoemission Spectroscopy Measurements.

The angle-resolved photoemission spectroscopy measurements were performed at beamline 9U (Dreamline) of the Shanghai Synchrotron Radiation Facility with a Scienta Omicron DA30L analyzer. The angle resolution was 0.1°, and the combined instrumental energy resolution was better than 20 meV. The photon energy used in our experiments ranged from 25 to 90 eV, and the measurements were conducted at 7 to 20 K. The ^{−11} mbar.

### Electronic Band Structure Calculations.

First-principles calculations were carried out within the framework of density functional theory using the Vienna Ab initio Simulation Package (45). All of the calculations were performed with a plane-wave cutoff of 450 eV on the 9 × 9 × 9 Γ-centered k-mesh, and the convergence criterion of energy was 10^{−6} eV. The generalized gradient approximation with the Perdew–Burke–Ernzerhof functional (46) was adopted to describe electron exchange and correlation. During structure optimization, all atoms were fully relaxed until the force on each atom was smaller than 0.01 eV/Å. In order to obtain a reliable band gap, the HSE06 hybrid functional (47) was used in the band structure calculation. The rotational symmetry *C*. The eigenvalue switches between the two bands at _{1} is protected by rotational symmetry. It is well known that the Kramers degeneracy is a twofold degeneracy at time-reversal-invariant momentum. Here, the Weyl point of W_{2} is at L point, which is a time-reversal-invariant momentum. Hence, the Weyl point of W_{2} is protected by time-reversal symmetry. To accurately calculate the Berry curvature in the Brillouin zone, we have fitted a Wannier tight-binding Hamiltonian by using the WANNIER90 package (48). The p orbitals of Te are used as the initial projectors for Wannier Hamiltonian construction. The chirality of a Weyl point is calculated by integrating the Berry curvature on a surface enclosing the Weyl point.

### Data Processing.

Due to the nonlinearity of Hall data, the carrier density was extracted from the linear part of the low-field Hall resistivity. Attempts to use the two-carrier fitting model were unsuccessful. For the log-periodic oscillations, the background was obtained through smoothing the MR/Hall data. The second derivative method is a widely adopted approach to confirm the exact positions of the extrema fields (21). We thus compared the extracted oscillations obtained via these two methods and obtained consistent results (*SI Appendix*, Fig. S15), demonstrating the validity of our data processing.

### Data Availability.

All data are available in the main text or *SI Appendix*.

## Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grants 11974324, U1832151, 11804326, 11774325, and 21603210), the Strategic Priority Research Program of Chinese Academy of Sciences (CAS) (Grant XDC07010000), the National Key Research and Development Program of China (Grants 2017YFA0403600 and 2017YFA0204904), the Anhui Initiative in Quantum Information Technologies (Grant AHY170000), Hefei Science Center CAS (Grant 2018HSC-UE014), the Anhui Provincial Natural Science Foundation (Grant 1708085QA20), the Fundamental Research Funds for the Central Universities (Grants WK2030040087 and WK3510000007), and the Science, Technology, and Innovation Commission of Shenzhen Municipality (Grant KQTD2016022619565991).

## Footnotes

↵

^{1}N.Z., G.Z., and L.L. contributed equally to this work.- ↵
^{2}To whom correspondence may be addressed. Email: lilin{at}ustc.edu.cn, zfwang15{at}ustc.edu.cn, or cgzeng{at}ustc.edu.cn.

Author contributions: L.L. and C.Z. designed research; N.Z., G.Z., L.L., P.W., L.X., B.C., H.L., Z.L., C.X., J.K., M.Y., J.H., and Z.S. performed research; N.Z., G.Z., L.L., Z.W., Z.Z., and C.Z. analyzed data; and N.Z., G.Z., L.L., Z.W., and C.Z. wrote the paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission. J.K. is a guest editor invited by the Editorial Board.

This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2002913117/-/DCSupplemental.

Published under the PNAS license.

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