Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5

Abstract

Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-field transport measurements of the Dirac semimetal candidate ZrTe₅ . Owing to the large g factor in ZrTe₅ , 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 ultra-quantum limit, where we observe abrupt changes in the magnetoresistance, indicating field-induced phase transitions. This is interpreted as an interaction-induced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in high-energy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters.

ARTICLE

Received 28 Feb 2016 | Accepted 11 Jul 2016 | Published 12 Aug 2016

Yanwen Liu1,2,3, Xiang Yuan1,2,3, Cheng Zhang1,2,3, Zhao Jin4, Awadhesh Narayan5,6, Chen Luo7, Zhigang Chen8,

Lei Yang8, Jin Zou8,9, Xing Wu7, Stefano Sanvito5, Zhengcai Xia4, Liang Li4, Zhong Wang10,11 & Faxian Xiu1,2,3

Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-eld transport measurements of the Dirac semimetal candidate ZrTe5. Owing to the large g factor in ZrTe5, the Zeeman splitting can be observed at magnetic eld as low as 3 T. Most prominently, high pulsed magnetic eld up to 60 T drives the system into the ultra-quantum limit, where we observe abrupt changes in the magnetoresistance, indicating eld-induced phase transitions. This is interpreted as an interaction-induced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in high-energy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters.

DOI: 10.1038/ncomms12516 OPEN

Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5

1 State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China. 2 Department of Physics, Fudan University, Shanghai 200433, China.

3 Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China. 4 Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China. 5 School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Ireland. 6 Department of Physics, University of Illinois at UrbanaChampaign, Urbana, Illinois 61801, USA. 7 Shanghai Key Laboratory of Multidimensional Information Processing, Department of Electrical Engineering, East China Normal University, Shanghai 200241, China. 8 Materials Engineering, The University of Queensland, Brisbane, Queensland 4072, Australia. 9 Centre for Microscopy and Microanalysis, The University of Queensland, Brisbane, Queensland 4072, Australia.

10 Institute for Advanced Study, Tsinghua University, Beijing 100084, China. 11 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China. Correspondence and requests for materials should be addressed to F.X. (email: mailto:[email protected]

Web End [email protected] ).

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In the past few decades, transition-metal pentatelluride ZrTe5 has attracted considerable attentions for its mysterious temperature anomaly1,2. Charge density wave was believed

to be the origin of the anomalous peak in the temperature-dependent resistance but later it was excluded by experiments2. At the same time, both theory3 and experiments46 demonstrated that the band structure of ZrTe5 is very complicated with multiple bands contributing to the electronic properties. Both single-frequency5,6 and multi-frequency4 Shubnikovde Haas (SdH) oscillations were reported in ZrTe5, suggesting a strong dependency of the electron states on the Fermi energy, EF, in the band structure.

Recently, this material was reinvestigated as a candidate of Dirac semimetal7. A linear energymomentum dispersion of the electronic structure in ZrTe5 was demonstrated by angle-resolved photoemission spectroscopy (ARPES)8 and optical spectroscopy measurements9,10. The negative magnetoresistance caused by chiral magnetic effect was also observed through magneto-transport8. These experimental evidences all suggest that ZrTe5 is a Dirac semimetal candidate, which is similar to other Dirac semimetals1116 with extremely large magnetoresistance1719 and the negative magnetoresistance8,2022 possibly induced by the chiral anomaly. Although the single-particle physics of Dirac semimetals, including ZrTe5 is under intense study, the many-body correlation effects are much less investigated. A high magnetic eld would signicantly 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 ZrTe5 in the high-magnetic eld regime. Possible phase transitions in high-magnetic elds have been reported in semimetallic graphite and bismuth2329, which, however, are not ideal Dirac semimetals. For Dirac and Weyl semimetals, it has been theoretically suggested that a high-magnetic eld may induce the dynamical mass generation3034, namely, a Dirac mass is spontaneously generated by interaction effects. Depending on material details, the Dirac mass can manifest itself as charge density wave30,33,35, spin density wave31 or nematic state34. Although the mass generation has been observed at the surface of two-dimensional (2D) topological crystalline insulators36,37, so far there is no clear evidence of its occurrence in three-dimensional bulk Dirac materials, despite its closer resemblance to that occurring in particle physics38. Moreover, dynamical mass generation in three-dimensional 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 modes35,39,40, holding promises to dissipationless transport inside three-dimensional bulk materials.

Here we report systematic transport measurements of single-crystal ZrTe5 under extremely large magnetic eld. Our samples show good crystalline quality and exhibit sufciently high electron mobility at low temperatures, enabling the observation of SdH oscillations under a relatively small magnetic eld. By tilting the eld direction, we mapped the morphology of the detected Fermi surface and examined the topological property of ZrTe5. The extracted band parameters suggest ZrTe5 to be a highly anisotropic material. Remarkably, with a weak magnetic eld 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 conned in the lowest Landau level. Under the magnetic eld, 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 ndings not only suggest ZrTe5 a versatile platform for searching novel correlated states in Dirac semimetal but also show the possibility on eld-controlled novel symmetry-breaking phases manifesting the Dirac mass in the study of Dirac and Weyl semimetals.

ResultsGrowth and hall-effect measurements. ZrTe5 single crystals were grown by chemical vapour transport with iodine as reported elsewhere41. The bulk ZrTe5 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 (D172h)7.

The ZrTe5 layers stack along the b axis. In the ac plane, ZrTe3 chains along a axis are connected by Te atoms in the c axis direction. Figure 1a is a typical high-resolution transmission electron microscopy (HRTEM) image taken from an as-grown layered sample, from which the high crystalline quality can be demonstrated. The inset selected area electron diffraction pattern together with the HRTEM image conrms that the layer normal is along the b axis.

The temperature dependence of the resistance Rxx and Hall

effect measurements provide information on the electronic states of a material in a succinct way. We rst carried out regular transport measurements to extract the fundamental band parameters of as-grown ZrTe5 crystals. In a Hall bar sample, the current was applied along the a axis and the magnetic eld was applied along the b axis (the stacking direction of the ZrTe5 layers). Figure 1b shows the temperature dependence of the resistance Rxx of ZrTe5 under the zero eld. An anomalous peak, the unambiguous hallmark of ZrTe5 (ref. 4), emerges at around 138 K and is ascribed to the temperature-dependent Fermi energy shift of the electronic band structure42. The Hall effect measurements provide more information on the charge carriers responsible for the transport. The Hall coefcient changes sign around the anomaly temperature, implying the dominant charge carriers changing from holes to electrons (Fig. 1c). The nonlinear Hall signal suggests a multi-carrier transport at both low and high temperatures, which is also conrmed by the Kohlers plot and our rst-principles electronic structure calculations (Supplementary Note 1 and Supplementary Figs 15). For convenience, a two-carrier transport model43,44 is adopted to estimate the carrier density and mobility. The dominant electron exhibits an ultrahigh mobility of around 50,000 cm2 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 one-tenth of that at low temperature, and nally holes become the majority carriers at T4138 K (Fig. 1d). Detailed analysis of the two-carrier transport is described in Supplementary Notes 1 and 2 and in Supplementary Figs 18.

Fermi surface and quantum oscillations analysis. Elaborate measurements of angle-dependent magnetoresistance (MR) provide further insight into the band-topological properties of ZrTe5. A different external magnetic eld geometry has been exploited to detect the Fermi surface at 2 K, as shown in Fig. 2. When the magnetic eld B40.5T is applied along the b axis, clear quantum oscillations can be identied, indicating a high mobility exceeding 20,000 cm2 V 1 s 1. The MR ratio RB R0R0 is around

10 (here R(B) is the resistance under magnetic eld B and R(0) is the resistance under zero eld), lower than previous results8 on account of different Fermi level positions. As the magnetic eld is tilted away from the b axis, the MR damps with the law of cosines, suggesting a quasi-2D nature and a highly anisotropic Fermi surface with the cigar/ellipsoid shape. This is reasonable for a

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Figure 1 | Crystal structure and Hall effect measurements of ZrTe5. (a) An HRTEM image of ZrTe5 with an inset selected area electron diffraction (SAED) pattern, showing the layer normal along the b axis. The white scale bar corresponds to 2 nm. (b) Temperature-dependent resistance under zero magnetic eld. An anomalous resistance peak occurs at TB138 K. (c) Temperature-dependent Hall resistance of ZrTe5. The nonlinear Hall slopes at both low temperature and high temperature demonstrate the multi-carrier transport in ZrTe5. (d) The temperature-dependent mobility and carrier density of the dominant carriers. A transition of electron- to hole-dominated transport is observed around the temperature of the anomalous resistance peak. The graduated background represents the amount and type of carriers, blue for holes and red for electrons.

layered material45. A Landau fan diagram of arbitrary angle (Fig. 2b) is plotted to extract the oscillation frequency SF and

Berrys phase FB according to the LifshitzOnsager quantization rule46: SFB N 12 FB2p d N g, where N is the Landau level

index, SF is obtained from the slope of Landau fan diagram and g is the intercept. For Dirac fermions, a value of |g| between 0 and 1/8 implies a non-trivial p Berrys phase46, whereas a value of around 0.5 represents a trivial Berrys phase. Here the integer indices denote the DRxx peak positions in 1/B, while half integer indices represent the DRxx valley positions. To avoid the inuence from the Zeeman effect, here we only consider the NZ3 Landau levels. With the magnetic eld along the b axis, the Landau fan diagram yields an intercept g of 0.140.05, exhibiting a nontrivial Berrys phase for the detected Fermi surface. At the same time, SF shows a small value of 4.8 T, corresponding to a tiny

Fermi area of 4.6 10 4 2. The system remains in the non

trivial Berrys phase as long as 0rbr70 (Fig. 2b inset and Fig. 2c). We have also obtained the angular dependence of SF as

illustrated in the inset of Fig. 2c where a good agreement with a 1/cosb relationship is reached, conrming a quasi-2D Fermi surface. However, as the magnetic eld is rotated towards the c axis (b470), the Berrys phase begins to deviate from the nontrivial and nally turns to be trivial when B is along the c axis (Fig. 2b inset, the two dark-red curves with intercept of B0.5).

Meanwhile, the oscillation frequency SF deviates from the cosines law and gives a value of 29.4 T along the c axis (Fig. 2c inset). The Berrys phase development along with the angular-dependent SF unveils the quasi-2D Dirac nature of ZrTe5 and possibly a nonlinear energy dispersion along the c axis. This is also conrmed 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 ZrTe5. Following the LifshitzKosevich formula4648, the oscillation component DRxx could be described by

DRxx pRTRDRS cos 2p SFB g

; 1

where RT, RD and RS are three reduction factors accounting for the phase smearing effect of temperature, scattering and spin splitting, respectively. Temperature-dependent oscillation DRxx could be captured by the temperature smearing factor RT /

2p2kBTm = eB sinh2p

2kBTm = eB, where kB is the Boltzmanns

constant, : is the reduced Planks constant and m* is the in-plane average cyclotron effective mass. By performing the best t of the thermal damping oscillation to the equation, the effective mass mac* (when the magnetic eld is applied along the b axis, the Fermi surface in ac plane is detected) is extracted to be 0.026me, where me 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 Dirac18,49,50 or Weyl semimetals19. The corresponding Fermi velocity yields a value of 5.2 105 m s 1, which agrees with recent ARPES

results42. A similar analysis gives a value of mab* 0.16me and

mbc* 0.26me, respectively (Fig. 2e; also see Supplementary

Note 3, Supplementary Figs 911 and Supplementary Table 1 for detailed information). Both mab* and mbc* are larger than mac*; this indicates a deviation from linear dispersion of these two surfaces considering the weak interlayer coupling7, which is in agreement with our previous results51 and the reported ARPES8. The carrier lifetime t could be obtained from the Dingle

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Figure 2 | Angular MR and SdH oscillations of ZrTe5. (a) Angular MR of ZrTe5. The inset shows the geometry of external magnetic eld. (b) Landau fan diagram of arbitrary angle in a. Inset: Zoom-in view of the intercept on y axis. (c) The angular-dependent intercept of Landau fan diagram in b. Inset: angular-dependent oscillation frequency. The error bars were generated from the linear tting process in the Landau fan diagrams. (d,e) The effective mass of ZrTe5 when the magnetic eld is applied along b axis and c axis, respectively. The error bars were generated from the tting process. (f) The quantum oscillations of Rxx and quantized plateaus in Rxy.

Table 1 | Band parameters of ZrTe5.

Geometry Effective mass Frequency Fermi area Fermi velocity Lifetime m*/me SF (T) AF( 2) vF (105 ms 1) s (ps)

bc plane 0.26 46.6 4.4 10 3 1.7 0.16

ac plane 0.026 4.8 4.6 10 4 5.2 0.13

ab plane 0.16 29.4 2.8 10 3 2.2 0.21

The band parameters, including the effective mass m*, Fermi surface S , Fermi area A , Fermi velocity v and lifetime s can be extracted from the SdH oscillations.

factor RDBe D, where D pm eBt. Table 1 summarizes the

analysed parameters of the band structure.Besides the obvious SdH oscillations of Rxx, Rxy exhibits

distinct nearly quantized plateaus, whose positions show a good alignment with the valley of Rxx (Fig. 2f). The value of 1/Rxy 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 n-doped Bi2Se3 (ref. 52), Z-Mo4O11 (ref. 53) and organic

Bechgaard salt5456. 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 interaction7, bulk

ZrTe5 behaves as a series of stacking parallel 2D electron channels with layered transport, which leads to the 2D-like magneto-transport as discussed above. The impurity or the coupling between the adjacent layers in the bulk causes the dissipation so that the Rxx cannot reach zero52. It is worth noting that the peak associated to the second Landau level in Rxx 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 eld. To investigate the spin splitting, it is necessary to further reduce the system temperature. Figure 3a

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Figure 3 | Zeeman splitting in ZrTe5. (a) MR behaviour of ZrTe5 at the temperature range of 0.263 K. (b) Temperature-dependent MR of ZrTe5. Two dashed lines are a guide to the eyes, which indicate the Zeeman splitting of the second Landau level. (c) The oscillation component in Rxy at 0.4 and 0.5 K.

Sizable Zeeman splitting can be distinguished from the second and third Landau levels. (d) Landau fan diagram for both spin-up and spin-down electrons. (e) Angular dependence of the rst-order differential Rxy versus 1/Bcosa. (f) The spacing of Zeeman splitting in the second Landau level at different eld angles. The inset shows the geometry of external magnetic eld.

shows the MR behaviour of ZrTe5 at 260 mK. A peak deriving from the rst Landau level can be observed at B6 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 Rxy signal provides a much clearer signal: after subtracting the MR background, it reveals strong Zeeman splitting from the oscillatory component DRxy (Fig. 3c and

Supplementary Fig. 12). At 0.4 K, the fth Landau level begins to exhibit a doublet structure with a broad feature. Under higher magnetic elds, 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 RS cospgm

2m0 is the phase difference between the oscillations of

spin-up and spin-down 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 results9. Given such a large g factor, it is understandable that the Zeeman splitting could be easily observed in a relatively weak magnetic eld. 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 eld is along the b axis (z direction), the Landau level energy eigenvalues for na0 are

En

E2k EB n

2

q , where mB is the Bohr

magneton, and in this case Ek :vzkz, EB

2 vxvyeB p

p gmBB=2

in equation (1) by the product-to-sum formula47 (detailed mathematical process is available in Supplementary Note 4). As a result, the oscillation component DRxx is equivalent to the superposition of the oscillations from the spin-up and spin-down Fermi surface

DRxxpRTRD cos 2p SFB g

1

2 j

cos 2p

is the

Landau level energy of the band bottom of the n 1 Landau level.

Here the Landau levels are split bygmBB, resulting in the observed Zeeman splitting.

The angular-dependence of the Zeeman splitting can provide valuable information to probe the underlying splitting mechanism. Figure 3e shows the rst-order differential Rxy as a function

of 1/Bcosa. Pronounced quantum oscillations with Zeeman splitting can be unambiguously distinguished and they align well with the scale of 1/Bcosa, further verifying the quasi-2D Fermi surface as mentioned before. It is noticeable that the spacing of

;

2

where j gm

SF

B g

1

2 j

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the Zeeman splitting changes with the eld angle. Generally, Zeeman splitting effect is believed to scale with the total external magnetic eld so that the spacing of the splitting Landau level would not change with angle. However, in the case of ZrTe5, the

spacing of the Zeeman splitting, normalized by Bcosa, is consistent with the quasi-2D nature (Fig. 3f). The angular dependent Zeeman splitting can be attributed to the orbital contribution caused by strong spin-orbit coupling in ZrTe5 (ref. 7). Regarding the effect of the exchange interaction induced by an external eld, we may decompose the splitting into an orbital-dependent and an orbital-independent part, where the former one depends on the shape of the band structure that leads to the angle-dependent splitting, and the latter one mainly comes from the Zeeman term that hardly contributes to any angular dependent splitting11. Owing to the highly anisotropic Fermi surface of ZrTe5 and the strong spin orbital coupling from the heavy Zr and Te atoms, the orbital effect in the ac plane of ZrTe5 is signicant, giving rise to a highly anisotropic g factor and an angular-dependent Zeeman splitting. Similar phenomena have also been observed in materials such as Cd3As2 (refs 49,57) and

Bi2Te3 (ref. 58).

Magnetotransport under high magnetic elds. A high magnetic eld up to 60 T was applied to drive the sample to the ultra-quantum limit to search for possible phase transitions. Figure 4a shows the angular-dependent MR of ZrTe5 under strong magnetic eld. The measurement geometry can be found in Fig. 3f inset. Several features are immediately prominent. First, when the

magnetic eld 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 eld is along the c axis, spin-splitting is hardly observed, again consistent with the theoretical expectations and the recent magneto-spectroscopy results9 (Supplementary Note 6 and Supplementary Fig. 14). Here the Landau level energy

eigenvalues become En

nE2B Ek gmBB=22

q , here

Ek :vyky. The effect of the magnetic eld is the horizontal

shifting of the degenerate Landau levels by gmBB/:vy in the ky vector direction (the eld direction), instead of splitting the heights of the band bottom like the case when the eld is along the a or b axis, thus there is no Landau level splitting in the quantum oscillation. Second, even with an external magnetic eld up to 60 T (in the quantum limit regime), the MR feature still follows the Bcosa tting, conrming once again the quasi-2D nature of ZrTe5 (Fig. 4b). Finally, and most importantly, a huge resistance peak emerges at around 8 T, followed by a at valley between 12 and 22 T, then the resistance increases and forms a shoulder-like peak at B30 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 rst Landau level has been submerged into the anomalous peak. Only a few materials show analogous eld-induced electronic instabilities, such as bismuth23,24,26, graphite25,29,59, and more recently the Weyl semimetal TaAs (ref. 60). As we have remarked,

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Figure 4 | Ultra-quantum limit transport and dynamical mass generation of ZrTe5 at 4.2 K. (a) Angular-dependent MR of ZrTe5 at 4.2 K under high magnetic eld up to 60 T. (b) Angular-dependent MR as a function of effective magnetic eld perpendicular to ac plane. (c,d) The Landau levels and Fermi levels for BE9 and 25 T, respectively. The inset of d is an illustration of the spin density wave from the n 0 Landau level.

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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 signicantly 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 23

! is slightly different from the

vector 14

!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 eld, 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 graphite61. In fact, if we take a simple BardeenCooperSchrieffer model for the density wave state, we have kBTc 1:14EF EB exp

1 N0V,

which predicts that Tc 0 as EF approaches EB, 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 eld increases, the density wave in the rst Landau level is destroyed because of such reentrant transition, consequently the resistance reduces.

Further increasing the magnetic eld to B 25 T, the resistivity

begins to increase sharply again (Fig. 4a). Since this phenomenon occurs in the ultra-quantum limit where almost all the electrons are conned 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 low-energy Hamiltonian H0k vxkxtxsz vykyty vzkztxsx

mtz,

form of density wave state directly in the future experiments such as spin-resolved scanning tunnelling microscopy. And such an exotic eld-induced density wave is also conrmed in HfTe5, which has a similar crystal structure and physical properties as ZrTe5 (More details are available in Supplementary Note 8 and Supplementary Figs 1618).

DiscussionFinally, let us briey compare ZrTe5 with the previously widely studied Dirac semimetals such as Cd3As2. In Cd3As2, it is difcult to observe such eld-induced density wave transitions with ultra-high magnetic eld49,62 because of their high Fermi velocity along any directions, leading to lower density of states insufcient to achieve pronounced density wave transitions or dynamical mass generation. In contrast, the strong anisotropy of ZrTe5 leads to an exotic layered transport and a quasi-2D Fermi surface. The consequent Fermi velocity along the b axis is very small, which strongly enhances the density of states when the magnetic eld is along the b axis. Another advantage of ZrTe5 is the relatively tiny

Fermi surface in ac plane, making it accessible to reach the low Landau level with relatively weak magnetic eld. With the strong magnetic eld, the electronelectron interaction can be efciently enhanced, amplifying the instability towards dynamical mass generation. The unambiguous Dirac feature in the ac plane together with the highly anisotropic Fermi velocity makes ZrTe5 an outstanding platform to study the eld-induced instabilities of Dirac fermions.

In summary, we have studied the transport properties of the newly discovered Dirac semimetal ZrTe5, and found signatures of the eld-induced dynamical mass generation. As a quasi-2D Dirac material with small Fermi velocity along the layered direction, ZrTe5 is an ideal material to explore eld-induced many-body effects. This study may open up a research avenue in the subject of Dirac and Weyl semimetals, namely, eld-controlled symmetry-breaking phases manifesting the Dirac mass. In the future, it will also be highly interesting to search for the topological dislocations35,39,40 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 elds.

Methods

Sample synthesis and characterizations. High-quality single crystals of ZrTe5 were grown via chemical vapour transport with iodine. Stoichiometric Zirconium ake (99.98%, Alfa Aesar) and Tellurium powder (99.999%, Alfa Aesar) were ground together and sealed in an evacuated quartz tube with iodine ake (99.995%, Alfa Aesar). A temperature gradient of 150 C between 580 and 430 C in a two-zone furnace was used for crystal growth. Typical as-grown sample has a long ribbon-like shape. HRTEM was carried out on JEM-2100F. An acceleration voltage of 200 kV was chosen to achieve enough resolution while maintaining the structure of ZrTe5.

Transport measurements. The low-eld magneto-transport measurements were performed in a Physical Property Measurement System by Quantum Design with a magnetic up to 9 T. The 60 T pulsed magnetic eld measurements were performed at Wuhan National High Magnetic Field Center.

Data availability. The data that support the ndings of this study are available from the corresponding author on request.

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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 Nano-fabrication Laboratory. Computational resources were provided by the Trinity Centre for High Performance Computing (TCHPC).

Author contributions

F.X. conceived the ideas and supervised the overall research; Y.L. and X.Y. synthetized ZrTe5 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. andX.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 co-authors.

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How to cite this article: Liu, Y. et al. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5. Nat. Commun. 7:12516 doi: 10.1038/ncomms12516 (2016).

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