Abstract
Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that manybody interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interactiondriven transition has been lacking. In this work, we report highmagneticfield transport measurements of the Dirac semimetal candidate ZrTe_{5}. Owing to the large g factor in ZrTe_{5}, the Zeeman splitting can be observed at magnetic field as low as 3 T. Most prominently, high pulsed magnetic field up to 60 T drives the system into the ultraquantum limit, where we observe abrupt changes in the magnetoresistance, indicating fieldinduced phase transitions. This is interpreted as an interactioninduced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in highenergy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters.
Introduction
In the past few decades, transitionmetal pentatelluride ZrTe_{5} has attracted considerable attentions for its mysterious temperature anomaly^{1,2}. Charge density wave was believed to be the origin of the anomalous peak in the temperaturedependent resistance but later it was excluded by experiments^{2}. At the same time, both theory^{3} and experiments^{4,5,6} demonstrated that the band structure of ZrTe_{5} is very complicated with multiple bands contributing to the electronic properties. Both singlefrequency^{5,6} and multifrequency^{4} Shubnikov–de Haas (SdH) oscillations were reported in ZrTe_{5}, suggesting a strong dependency of the electron states on the Fermi energy, E_{F}, in the band structure.
Recently, this material was reinvestigated as a candidate of Dirac semimetal^{7}. A linear energy–momentum dispersion of the electronic structure in ZrTe_{5} was demonstrated by angleresolved photoemission spectroscopy (ARPES)^{8} and optical spectroscopy measurements^{9,10}. The negative magnetoresistance caused by chiral magnetic effect was also observed through magnetotransport^{8}. These experimental evidences all suggest that ZrTe_{5} is a Dirac semimetal candidate, which is similar to other Dirac semimetals^{11,12,13,14,15,16} with extremely large magnetoresistance^{17,18,19} and the negative magnetoresistance^{8,20,21,22} possibly induced by the chiral anomaly. Although the singleparticle physics of Dirac semimetals, including ZrTe_{5} is under intense study, the manybody correlation effects are much less investigated. A high magnetic field would significantly enhance the density of states near the Fermi level, thus effectively amplifying the correlation effects. It is therefore highly desirable to investigate the behaviour of ZrTe_{5} in the highmagnetic field regime. Possible phase transitions in highmagnetic fields have been reported in semimetallic graphite and bismuth^{23,24,25,26,27,28,29}, which, however, are not ideal Dirac semimetals. For Dirac and Weyl semimetals, it has been theoretically suggested that a highmagnetic field may induce the dynamical mass generation^{30,31,32,33,34}, namely, a Dirac mass is spontaneously generated by interaction effects. Depending on material details, the Dirac mass can manifest itself as charge density wave^{30,33,35}, spin density wave^{31} or nematic state^{34}. Although the mass generation has been observed at the surface of twodimensional (2D) topological crystalline insulators^{36,37}, so far there is no clear evidence of its occurrence in threedimensional bulk Dirac materials, despite its closer resemblance to that occurring in particle physics^{38}. Moreover, dynamical mass generation in threedimensional Dirac semimetals hosts a number of unusual phenomena absent in two dimensions, for instance, it is expected that the topological dislocations associated with the dynamically generated mass may possess chiral modes^{35,39,40}, holding promises to dissipationless transport inside threedimensional bulk materials.
Here we report systematic transport measurements of singlecrystal ZrTe_{5} under extremely large magnetic field. Our samples show good crystalline quality and exhibit sufficiently high electron mobility at low temperatures, enabling the observation of SdH oscillations under a relatively small magnetic field. By tilting the field direction, we mapped the morphology of the detected Fermi surface and examined the topological property of ZrTe_{5}. The extracted band parameters suggest ZrTe_{5} to be a highly anisotropic material. Remarkably, with a weak magnetic field the spin degeneracy is lifted, generating a pronounced Zeeman splitting. Furthermore, by taking advantage of the tiny Fermi surface, this material can be driven into its quantum limit regime within 20 T, where all the carriers are confined in the lowest Landau level. Under the magnetic field, we observe sharp peaks in the resistivity, which are naturally explained as dynamical mass generation coming from Fermi surface nesting. The generated Dirac mass endows an energy gap to the nominally massless Dirac electrons, causing sharp increase in the resistivity. These findings not only suggest ZrTe_{5} a versatile platform for searching novel correlated states in Dirac semimetal but also show the possibility on fieldcontrolled novel symmetrybreaking phases manifesting the Dirac mass in the study of Dirac and Weyl semimetals.
Results
Growth and halleffect measurements
ZrTe_{5} single crystals were grown by chemical vapour transport with iodine as reported elsewhere^{41}. The bulk ZrTe_{5} has an orthorhombic layered structure with the lattice parameters of a=0.38 nm, b=1.43 nm, c=1.37 nm and a space group of Cmcm ()^{7}. The ZrTe_{5} layers stack along the b axis. In the a–c plane, ZrTe_{3} chains along a axis are connected by Te atoms in the c axis direction. Figure 1a is a typical highresolution transmission electron microscopy (HRTEM) image taken from an asgrown layered sample, from which the high crystalline quality can be demonstrated. The inset selected area electron diffraction pattern together with the HRTEM image confirms that the layer normal is along the b axis.
The temperature dependence of the resistance R_{xx} and Hall effect measurements provide information on the electronic states of a material in a succinct way. We first carried out regular transport measurements to extract the fundamental band parameters of asgrown ZrTe_{5} crystals. In a Hall bar sample, the current was applied along the a axis and the magnetic field was applied along the b axis (the stacking direction of the ZrTe_{5} layers). Figure 1b shows the temperature dependence of the resistance R_{xx} of ZrTe_{5} under the zero field. An anomalous peak, the unambiguous hallmark of ZrTe_{5} (ref. 4), emerges at around 138 K and is ascribed to the temperaturedependent Fermi energy shift of the electronic band structure^{42}. The Hall effect measurements provide more information on the charge carriers responsible for the transport. The Hall coefficient changes sign around the anomaly temperature, implying the dominant charge carriers changing from holes to electrons (Fig. 1c). The nonlinear Hall signal suggests a multicarrier transport at both low and high temperatures, which is also confirmed by the Kohler’s plot and our firstprinciples electronic structure calculations (Supplementary Note 1 and Supplementary Figs 1–5). For convenience, a twocarrier transport model^{43,44} is adopted to estimate the carrier density and mobility. The dominant electron exhibits an ultrahigh mobility of around 50,000 cm^{2} V^{−1} s^{−1} at low temperature, which leads to strong SdH oscillations as we will discuss later. Around the temperature of the resistance anomaly, the electron carrier density has already decayed to almost onetenth of that at low temperature, and finally holes become the majority carriers at T>138 K (Fig. 1d). Detailed analysis of the twocarrier transport is described in Supplementary Notes 1 and 2 and in Supplementary Figs 1–8.
Fermi surface and quantum oscillations analysis
Elaborate measurements of angledependent magnetoresistance (MR) provide further insight into the bandtopological properties of ZrTe_{5}. A different external magnetic field geometry has been exploited to detect the Fermi surface at 2 K, as shown in Fig. 2. When the magnetic field B>0.5T is applied along the b axis, clear quantum oscillations can be identified, indicating a high mobility exceeding 20,000 cm^{2} V^{−1} s^{−1}. The MR ratio is around 10 (here R(B) is the resistance under magnetic field B and R(0) is the resistance under zero field), lower than previous results^{8} on account of different Fermi level positions. As the magnetic field is tilted away from the b axis, the MR damps with the law of cosines, suggesting a quasi2D nature and a highly anisotropic Fermi surface with the cigar/ellipsoid shape. This is reasonable for a layered material^{45}. A Landau fan diagram of arbitrary angle (Fig. 2b) is plotted to extract the oscillation frequency S_{F} and Berry’s phase Φ_{B} according to the Lifshitz–Onsager quantization rule^{46}: , where N is the Landau level index, S_{F} is obtained from the slope of Landau fan diagram and γ is the intercept. For Dirac fermions, a value of γ between 0 and 1/8 implies a nontrivial π Berry’s phase^{46}, whereas a value of around 0.5 represents a trivial Berry’s phase. Here the integer indices denote the ΔR_{xx} peak positions in 1/B, while half integer indices represent the ΔR_{xx} valley positions. To avoid the influence from the Zeeman effect, here we only consider the N≥3 Landau levels. With the magnetic field along the b axis, the Landau fan diagram yields an intercept γ of 0.14±0.05, exhibiting a nontrivial Berry’s phase for the detected Fermi surface. At the same time, S_{F} shows a small value of 4.8 T, corresponding to a tiny Fermi area of 4.6 × 10^{−4} Å^{−2}. The system remains in the nontrivial Berry’s phase as long as 0≤β≤70° (Fig. 2b inset and Fig. 2c). We have also obtained the angular dependence of S_{F} as illustrated in the inset of Fig. 2c where a good agreement with a 1/cosβ relationship is reached, confirming a quasi2D Fermi surface. However, as the magnetic field is rotated towards the c axis (β>70°), the Berry’s phase begins to deviate from the nontrivial and finally turns to be trivial when B is along the c axis (Fig. 2b inset, the two darkred curves with intercept of ∼0.5). Meanwhile, the oscillation frequency S_{F} deviates from the cosines law and gives a value of 29.4 T along the c axis (Fig. 2c inset). The Berry’s phase development along with the angulardependent S_{F} unveils the quasi2D Dirac nature of ZrTe_{5} and possibly a nonlinear energy dispersion along the c axis. This is also confirmed by the band parameters such as the effective mass and the Fermi velocity, as described below.
A meticulous analysis of the oscillation amplitude at different angles was conducted to reveal the electronic band structure of ZrTe_{5}. Following the Lifshitz–Kosevich formula^{46,47,48}, the oscillation component ΔR_{xx} could be described by
where R_{T}, R_{D} and R_{S} are three reduction factors accounting for the phase smearing effect of temperature, scattering and spin splitting, respectively. Temperaturedependent oscillation ΔR_{xx} could be captured by the temperature smearing factor , where k_{B} is the Boltzmann’s constant, ħ is the reduced Plank’s constant and m* is the inplane average cyclotron effective mass. By performing the best fit of the thermal damping oscillation to the equation, the effective mass m_{a–c}* (when the magnetic field is applied along the b axis, the Fermi surface in a–c plane is detected) is extracted to be 0.026m_{e}, where m_{e} is the free electron mass (Fig. 2d). Such a small effective mass agrees well with the Dirac nature along this direction; and it is comparable to previously reported Dirac^{18,49,50} or Weyl semimetals^{19}. The corresponding Fermi velocity yields a value of 5.2 × 10^{5} m s^{−1}, which agrees with recent ARPES results^{42}. A similar analysis gives a value of m_{a–b}*=0.16m_{e} and m_{b–c}*=0.26m_{e}, respectively (Fig. 2e; also see Supplementary Note 3, Supplementary Figs 9–11 and Supplementary Table 1 for detailed information). Both m_{a–b}* and m_{b–c}* are larger than m_{a–c}*; this indicates a deviation from linear dispersion of these two surfaces considering the weak interlayer coupling^{7}, which is in agreement with our previous results^{51} and the reported ARPES^{8}. The carrier lifetime τ could be obtained from the Dingle factor R_{D}∼e^{−D}, where . Table 1 summarizes the analysed parameters of the band structure.
Besides the obvious SdH oscillations of R_{xx}, R_{xy} exhibits distinct nearly quantized plateaus, whose positions show a good alignment with the valley of R_{xx} (Fig. 2f). The value of 1/R_{xy} establishes a strict linearity of the index plot and demonstrates the excellent quantization (Fig. 2f inset), reminiscent of the bulk quantum Hall effect. A similar behaviour has been observed in several highly anisotropic layered materials, such as the heavily ndoped Bi_{2}Se_{3} (ref. 52), ηMo_{4}O_{11} (ref. 53) and organic Bechgaard salt^{54,55,56}. At variance with the quantum Hall effect in a 2D electron gas, the quantization of the inverse Hall resistance does not strictly correspond to the quantum conductance. In fact, because of the weak interlayer interaction^{7}, bulk ZrTe_{5} behaves as a series of stacking parallel 2D electron channels with layered transport, which leads to the 2Dlike magnetotransport as discussed above. The impurity or the coupling between the adjacent layers in the bulk causes the dissipation so that the R_{xx} cannot reach zero^{52}. It is worth noting that the peak associated to the second Landau level in R_{xx} displays a broad feature with two small corners marked by the arrows, implying the emergence of spin splitting.
Zeeman splitting under extremely low temperature
It is quite remarkable that the spin degeneracy can be removed by such a weak magnetic field. To investigate the spin splitting, it is necessary to further reduce the system temperature. Figure 3a shows the MR behaviour of ZrTe_{5} at 260 mK. A peak deriving from the first Landau level can be observed at ∼6 T. The second Landau level offers a better view of the Zeeman splitting because of the relatively small MR background, as marked by the dashed lines in Fig. 3b. The R_{xy} signal provides a much clearer signal: after subtracting the MR background, it reveals strong Zeeman splitting from the oscillatory component ΔR_{xy} (Fig. 3c and Supplementary Fig. 12). At 0.4 K, the fifth Landau level begins to exhibit a doublet structure with a broad feature. Under higher magnetic fields, the separation of the doublet structure increases, in particular, the second Landau level completely evolves into two peaks, indicating the complete lifting of spin degeneracy due to the Zeeman effect. To analyse the Zeeman effect occurred at such low temperature conveniently, we rearranged the spin phase factor in equation (1) by the producttosum formula^{47} (detailed mathematical process is available in Supplementary Note 4). As a result, the oscillation component ΔR_{xx} is equivalent to the superposition of the oscillations from the spinup and spindown Fermi surface
where is the phase difference between the oscillations of spinup and spindown electrons. With this method we can estimate the g factor by Landau index plot for both spin ladders (Fig. 3d). This leads to the g factor of 21.3, in good agreement with the optical results^{9}. Given such a large g factor, it is understandable that the Zeeman splitting could be easily observed in a relatively weak magnetic field. We have further carried out the theoretical Landau level calculations, which provides a clear insight into the Zeeman splitting as elaborated in Supplementary Note 5. In short, when the magnetic field is along the b axis (z direction), the Landau level energy eigenvalues for n≠0 are , where μ_{B} is the Bohr magneton, and in this case E_{k}=ħv_{z}k_{z}, is the Landau level energy of the band bottom of the n=1 Landau level. Here the Landau levels are split by, resulting in the observed Zeeman splitting.
The angulardependence of the Zeeman splitting can provide valuable information to probe the underlying splitting mechanism. Figure 3e shows the firstorder differential R_{xy} as a function of 1/Bcosα. Pronounced quantum oscillations with Zeeman splitting can be unambiguously distinguished and they align well with the scale of 1/Bcosα, further verifying the quasi2D Fermi surface as mentioned before. It is noticeable that the spacing of the Zeeman splitting changes with the field angle. Generally, Zeeman splitting effect is believed to scale with the total external magnetic field so that the spacing of the splitting Landau level would not change with angle. However, in the case of ZrTe_{5}, the spacing of the Zeeman splitting, normalized by Bcosα, is consistent with the quasi2D nature (Fig. 3f). The angular dependent Zeeman splitting can be attributed to the orbital contribution caused by strong spinorbit coupling in ZrTe_{5} (ref. 7). Regarding the effect of the exchange interaction induced by an external field, we may decompose the splitting into an orbitaldependent and an orbitalindependent part, where the former one depends on the shape of the band structure that leads to the angledependent splitting, and the latter one mainly comes from the Zeeman term that hardly contributes to any angular dependent splitting^{11}. Owing to the highly anisotropic Fermi surface of ZrTe_{5} and the strong spin orbital coupling from the heavy Zr and Te atoms, the orbital effect in the a–c plane of ZrTe_{5} is significant, giving rise to a highly anisotropic g factor and an angulardependent Zeeman splitting. Similar phenomena have also been observed in materials such as Cd_{3}As_{2} (refs 49, 57) and Bi_{2}Te_{3} (ref. 58).
Magnetotransport under high magnetic fields
A high magnetic field up to 60 T was applied to drive the sample to the ultraquantum limit to search for possible phase transitions. Figure 4a shows the angulardependent MR of ZrTe_{5} under strong magnetic field. The measurement geometry can be found in Fig. 3f inset. Several features are immediately prominent. First, when the magnetic field is along the a axis, Zeeman splitting is observed, which is consistent with the theoretically solved Landau levels (Supplementary Note 5). The g factor along the a axis extracted by formula (2) is 3.19, which agrees well with the anisotropy of g factor discussed above (Supplementary Fig. 13). When the magnetic field is along the c axis, spinsplitting is hardly observed, again consistent with the theoretical expectations and the recent magnetospectroscopy results^{9} (Supplementary Note 6 and Supplementary Fig. 14). Here the Landau level energy eigenvalues become , here E_{k}=ħv_{y}k_{y}. The effect of the magnetic field is the horizontal shifting of the degenerate Landau levels by ±gμ_{B}B/ħv_{y} in the k_{y} vector direction (the field direction), instead of splitting the heights of the band bottom like the case when the field is along the a or b axis, thus there is no Landau level splitting in the quantum oscillation. Second, even with an external magnetic field up to 60 T (in the quantum limit regime), the MR feature still follows the Bcosα fitting, confirming once again the quasi2D nature of ZrTe_{5} (Fig. 4b). Finally, and most importantly, a huge resistance peak emerges at around 8 T, followed by a flat valley between 12 and 22 T, then the resistance increases and forms a shoulderlike peak at ∼30 T. It should be emphasized that the amplitude of the resistance at 8 T is much larger than the amplitude of SdH oscillations, so that the signal of the first Landau level has been submerged into the anomalous peak. Only a few materials show analogous fieldinduced electronic instabilities, such as bismuth^{23,24,26}, graphite^{25,29,59}, and more recently the Weyl semimetal TaAs (ref. 60). As we have remarked, the SdH peak due to the n=1 Landau level merges into the anomalously large peak around B=8 T, which suggests that the n=2 Landau levels are empty and the electrons in the n=1 Landau level are responsible for the anomalous peak. The location of Fermi level is schematically shown in Fig. 4c. The peak can be naturally explained by the picture of dynamical mass generation (accompanied by a density wave formation, with the wave vector being the nesting vector) in the n=1 Landau levels, which leads to the generation of an energy gap for the electrons in these Landau levels, thus significantly enhancing the resistivity. In Fig. 4c, we illustrate one of the possibilities of nesting vectors responsible for this instability (the other possibility being two vectors connecting the Fermi momenta 1 to 3, and 2 to 4, respectively). Since the vector is slightly different from the vector due to the Zeeman splitting, the density wave transition should also be Zeeman split, which is presumably responsible for the existence of a ‘bump’ near the top of the peak in Fig. 2a.
On further increasing the magnetic field, the resistivity reaches a minimum at around B=14 T (Fig. 4b), which can be explained as a reentrant transition due to the crossing of the Fermi level with the band bottom of the n=1 Landau level. A similar phenomenon has been observed in graphite^{61}. In fact, if we take a simple Bardeen–Cooper–Schrieffer model for the density wave state, we have , which predicts that T_{c}=0 as E_{F} approaches E_{B}, leading to the destruction of density waves. Here N(0) and V are the density of states at the Fermi level and the interaction parameter (of the order of several eV), respectively. As the magnetic field increases, the density wave in the first Landau level is destroyed because of such reentrant transition, consequently the resistance reduces.
Further increasing the magnetic field to B=25 T, the resistivity begins to increase sharply again (Fig. 4a). Since this phenomenon occurs in the ultraquantum limit where almost all the electrons are confined in the n=0 Landau level, it can be explained as a dynamical mass generation in the n=0 Landau level. The nesting vector of this density wave transition is shown in Fig. 4d. The explicit form of the density wave is inaccessible by the transport experiments, nevertheless, we can theoretically calculate it following ref. 24. With the lowenergy Hamiltonian , where the Pauli matrices τ_{x,y,z} refers to certain orbital degrees of freedom and σ_{x,y,z} represents the electron spin, and m is a mass parameter that is almost zero. The x, y, z axes correspond to a, c, b axes of the crystal, respectively. Then we have the Landau level wave functions for the zeroth Landau level:
Here θ_{k} satisfies tanθ_{k}=E_{k}/E_{k}, and E_{z}=μ_{B}gB/2. Inserting the wave function (3) into the zcomponent of the spin density we have (Supplementary Note 7 and Supplementary Fig. 15)
where α_{0} is a constant phase angle and the constant m_{0} can be taken as the order parameter of the density wave. For the first Landau level, the density wave also has the similar form of . It would be interesting to demonstrate the form of density wave state directly in the future experiments such as spinresolved scanning tunnelling microscopy. And such an exotic fieldinduced density wave is also confirmed in HfTe_{5}, which has a similar crystal structure and physical properties as ZrTe_{5} (More details are available in Supplementary Note 8 and Supplementary Figs 16–18).
Discussion
Finally, let us briefly compare ZrTe_{5} with the previously widely studied Dirac semimetals such as Cd_{3}As_{2}. In Cd_{3}As_{2}, it is difficult to observe such fieldinduced density wave transitions with ultrahigh magnetic field^{49,62} because of their high Fermi velocity along any directions, leading to lower density of states insufficient to achieve pronounced density wave transitions or dynamical mass generation. In contrast, the strong anisotropy of ZrTe_{5} leads to an exotic layered transport and a quasi2D Fermi surface. The consequent Fermi velocity along the b axis is very small, which strongly enhances the density of states when the magnetic field is along the b axis. Another advantage of ZrTe_{5} is the relatively tiny Fermi surface in a–c plane, making it accessible to reach the low Landau level with relatively weak magnetic field. With the strong magnetic field, the electron–electron interaction can be efficiently enhanced, amplifying the instability towards dynamical mass generation. The unambiguous Dirac feature in the a–c plane together with the highly anisotropic Fermi velocity makes ZrTe_{5} an outstanding platform to study the fieldinduced instabilities of Dirac fermions.
In summary, we have studied the transport properties of the newly discovered Dirac semimetal ZrTe_{5}, and found signatures of the fieldinduced dynamical mass generation. As a quasi2D Dirac material with small Fermi velocity along the layered direction, ZrTe_{5} is an ideal material to explore fieldinduced manybody effects. This study may open up a research avenue in the subject of Dirac and Weyl semimetals, namely, fieldcontrolled symmetrybreaking phases manifesting the Dirac mass. In the future, it will also be highly interesting to search for the topological dislocations^{35,39,40} of the dynamically generated mass, which may host the dissipationless chiral modes. In a wider perspective, this study shows the possibility of investigating and engineering interaction effects in topological materials, topological semimetals in particular, by applying external fields.
Methods
Sample synthesis and characterizations
Highquality single crystals of ZrTe_{5} were grown via chemical vapour transport with iodine. Stoichiometric Zirconium flake (99.98%, Alfa Aesar) and Tellurium powder (99.999%, Alfa Aesar) were ground together and sealed in an evacuated quartz tube with iodine flake (99.995%, Alfa Aesar). A temperature gradient of 150 °C between 580 and 430 °C in a twozone furnace was used for crystal growth. Typical asgrown sample has a long ribbonlike shape. HRTEM was carried out on JEM2100F. An acceleration voltage of 200 kV was chosen to achieve enough resolution while maintaining the structure of ZrTe_{5}.
Transport measurements
The lowfield magnetotransport measurements were performed in a Physical Property Measurement System by Quantum Design with a magnetic up to 9 T. The 60 T pulsed magnetic field measurements were performed at Wuhan National High Magnetic Field Center.
Data availability
The data that support the findings of this study are available from the corresponding author on request.
Additional information
How to cite this article: Liu, Y. et al. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe_{5}. Nat. Commun. 7:12516 doi: 10.1038/ncomms12516 (2016).
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Acknowledgements
This work was supported by the National Young 1000 Talent Plan and National Natural Science Foundation of China (61322407 and 11474058). F.X. acknowledges the support from the open project of Wuhan National High Magnetic Field Center (#PHMFF2015003). X.W. acknowledges the support from National Natural Science Foundation of China (11504111 and 61574060), Projects of Science and Technology Commission of Shanghai Municipality Grant (15JC1401800) and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning. A.N. acknowledges support from the Irish Research Council under the EMBARK initiative. S.S. acknowledges support from the European Research Council (QUEST project). Z.W. acknowledges support from National Natural Science Foundation of China (No.11304175). Part of the sample fabrication was performed at Fudan Nanofabrication Laboratory. Computational resources were provided by the Trinity Centre for High Performance Computing (TCHPC).
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F.X. conceived the ideas and supervised the overall research; Y.L. and X.Y. synthetized ZrTe_{5} single crystals; Y.L., X.Y., C.Z. and J.Z. performed the magnetotransport measurements and analysed the transport data; Zhigang Chen., L.Y., Jin Zou. C.L. and X.W. performed crystal structural analysis; A.N. and S.S. performed the band structure and Fermi surface calculations; Z.W. provided the theoretical calculations and explanations for the magnetotransport; Z.X. and L.L. gave suggestions and guidance of experiments; Y.L. and F.X. wrote the paper with helps from all other coauthors.
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Supplementary Figures 118, Supplementary Table 1, Supplementary Notes 18 and Supplementary References. (PDF 3412 kb)
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Liu, Y., Yuan, X., Zhang, C. et al. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe_{5}. Nat Commun 7, 12516 (2016). https://doi.org/10.1038/ncomms12516
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DOI: https://doi.org/10.1038/ncomms12516
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