Optical spectroscopy study of three dimensional Dirac semimetal ZrTe 5
R. Y. Chen, S. J. Zhang, J. A. Schneeloch, C. Zhang, Q. Li, G. D. Gu, N. L. Wang
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A ug Optical spectroscopy study of three dimensional Dirac semimetal ZrTe R. Y. Chen, S. J. Zhang, J. A. Schneeloch, C. Zhang, Q. Li, G. D. Gu, and N. L. Wang
1, 3 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China Condensed Matter Physics and Materials Science Department,Brookhaven National Lab, Upton, New York 11973, USA Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
Three dimensional (3D) topological Dirac materials are under intensive study recently. The layered compoundZrTe has been suggested to be one of them by transport and ARPES experiments. Here, we perform infraredreflectivity measurement to investigate the underlying physics of this material. The derived optical conductivityexhibits linear increasing with frequency below normal interband transitions, which provides the first opticalspectroscopic proof of a 3D Dirac semimetal. Apart from that, the plasma edge shifts dramatically to lowerenergy upon temperature cooling, which might be associated with the consequence shrinking of the latticeparameters. In addition, an extremely sharp peak shows up in the frequency dependent optical conductivity,indicating the presence of a Van Hove singularity in the joint density of state. PACS numbers: 71.55.Ak, 78.20.-e,72.15.Eb
Three dimensional (3D) topological Dirac materials, suchas Dirac semimetals and Weyl semimetals, have attractedtremendous attention in condensed matter physics and mate-rials science in recent years. The 3D Dirac semimetals pos-sess 3D Dirac nodes where the valence and conduction bandstouch along certain symmetric axis. The 3D Dirac node isprotected against gap formation by crystalline symmetry andcan be considered as two overlapped Weyl nodes of oppositechirality [1, 2]. The materials are expected to host many in-triguing novel phenomena and properties, such as the appear-ance of Fermi arcs on the surfaces [3], giant diamagnetism[4, 5], and very large linear magnetoresistance [6, 7]. Whentime reversal symmetry is broken, a 3D Dirac semimetal canbe driven to a Weyl semimetal. This has stimulated stronginterest to explore chiral magnetic e ff ect [8–15], i. e. thecharge-pumping between Weyl nodes of opposite chiralitiesunder magnetic field, which is a macroscopic manifestationof the quantum anomaly in relativistic field theory of chiralfermions.Only a few materials were predicted to be 3D Diracsemimetals. Among them, Na Bi and Cd As are the twobest known compounds [16, 17]. They were confirmed to be3D Dirac semimetals by angle-resolved photoemission spec-troscopy (ARPES) experiments [18–21]. Very recently, an-other layered compound, ZrTe , was suggested to be also a3D Dirac semimetal based on transport and ARPES experi-ments [13]. ZrTe crystallizes in the layered orthorhombiccrystal structure, with prismatic ZrTe chains running alongthe crystallographic a-axis and linked along the c-axis viazigzag chains of Te atoms to form two-dimensional (2D) lay-ers. Those layers stack along the b-axis. Most attractively, thechiral magnetic e ff ect was clearly observed for the first timeon ZrTe through a magneto-transport measurement [13].The 3D band dispersions in Dirac semimetals enable thebulk measurement techniques, e.g. the optical spectroscopymeasurement, to provide key information about the chargeproperties of the materials. For any electronic material, suchinformation is of crucial importance for understanding under- lying physics. The situation would be di ff erent from the in-vestigations on 3D topological insulators where the focus is onthe non-trivial surface state. For those materials, the bulk mea-surement technique could hardly detect or separate the con-tribution from the 2D Dirac fermions of topological surfacestates, as a result, the experimental probes were largely lim-ited to surface sensitive measurements like ARPES or scan-ning tunneling microscopy (STM).Although a 3D Dirac semimetal could be viewed as a bulkanalogue of 2D graphene in terms of band dispersions, akey di ff erence exists in charge dynamical properties between2D and 3D Dirac fermions. For 2D Dirac fermions like ingraphene, the real part of conductivity is well known to bea frequency independent quantity [22], while for 3D Diracfermions with linear band dispersions in all three momentumdirections, the real part of conductivity grows linearly withthe frequency [23, 24]. To our knowledge, no optical spectro-scopic measurement has been reported on 3D Dirac semimet-als. In this work we present temperature and frequency depen-dent optical spectroscopy study on ZrTe . Our study revealsseveral peculiar features. The density of free carriers keepsdropping with temperature decreasing and an unusual sharp m c m ) T (K)
ZrTe I // a-axis
FIG. 1: Temperature dependent resistivity of ZrTe along a-axis. (a) (a) R ( cm -1 ) 300 K R (cm -1 )
300 K 200 K 150 K 80 K 50 K 8 K R ( cm -1 )
300 K 200 K 150 K 80 K 50 K 8 K R ( cm -1 )
300 K 200 K 150 K 80 K 50 K 8 K (b) (c)
FIG. 2: Temperature dependent optical reflectivity R ( ω ) below 600 cm − along a - (panel a) and c -axis (panel b). Panel (c) displays R ( ω ) below10000 cm − along a axis, while the inset shows the spectrum up to 50000 cm − at room temperature. peak shows up in the reflectivity and conductivity spectra inthe mid-infrared region. Of most importance, the linear ris-ing of the optical conductivity is observed in a relatively largeenergy scale, just as expected for a 3D Dirac semimetal.Single crystals ZrTe were grown by using Te fluxmethod. 100 grams high purity 7N (99.99999%) Te and 6N(99.9999%) Zr were loaded into 20 mm diameter double-walled quartz ampoules with 200 mm length and sealed undervacuum. The composition of the Zr-Te solution for the ZrTe crystal growth is Zr . Te . , and the largest ZrTe singlecrystals obtained are around ∼ × ×
20 mm . Detailedgrowth procedure was described elsewhere [13].Figure 1 displays the dc resistivity in the chain directionas a function of temperature of ZrTe . The resistivity curveshows rather unusual features. With decreasing temperaturefrom 300 K, ρ ( T ) decreases slightly first, then increases be-low roughly 200 K and reaches a peak near 60 K. The over-all small values of ρ ( T ) signal the (semi)metallic nature ofthe compound, which are in consistent with the optical mea-surements presented below. In earlier reports, the resistivitypeak located near 150 - 170 K [25, 26]. The much lower peaktemperature could be attributed to a much lower defects inthe present sample. The unusual features are likely associatedwith its characteristic electronic structure, which could be sen-sitive to the temperature-induced structural change. Earlierband structure calculations suggested presence of extremelysmall and light ellipsoidal Fermi surfaces, centered at the cen-ter ( Γ point) of the bulk Brillouin zone (BBZ) [27], and quan-tum oscillation measurements indicated three tiny but finiteFermi surfaces [26], with the e ff ective mass in the chain di-rection (m ∗ a ≃ e ) being comparable to that in a prototyp-ical 3D Dirac semimetal, Cd As [28]. More recent ab initio calculations indicated that ZrTe compound locates close tothe phase boundary between weak and strong topological in-sulators [29]. Nevertheless, very recent transport and ARPESexperiments identify it to be a 3D Dirac semimetal [13].The polarized optical reflectance measurements with E // a -axis and E // c -axis were performed respectively on a combi-nation of Bruke 113V, 80V and grating-type spectrometer inthe frequency range from 30-50 000 cm − . The reflectivityalong a - and c -axis in the far-infrared region are displayed in Fig. 2 (a) and (b), respectively. The a -axis reflectivity overbroad energy scales is shown in Fig. 2 (c). There are severalprominent phonon absorption features lying below 200 cm − ,which get more pronounced upon cooling. At room temper-ature, the reflectivity R ( ω ) shows a well-defined plasma edgebelow 350 cm − and approaches unity at low frequency. Thisindicates clearly a metallic response, which is consistent withthe results of transport measurements. The edge frequency,being usually referred to as ”screened” plasma frequency, isrelated to the density n and e ff ective mass m ∗ of free carri-ers by ω ′ p ∝ n / m ∗ . The unusual low value of this frequencysuggests a very small n . As the temperature decreases, theedge shifts to lower frequency, indicating a further reductionof the number of free carriers. Below 80 K, the extremelystrong phonon signals tend to blur the plasma edge. In themeantime, the carrier scattering rate is also reduced as the re-flectance edge gets steeper. The combination of the two ef-fects is likely the driving force of the broad peak appeared at60 K in ρ ( T ). Furthermore, the rapid reduction of the plasmafrequency yields optical evidence that the compound tend toapproach the semimetal state at very low temperature.R( ω ) along the c axis shows similar behaviors as along the a axis. The plasma edge almost lies at the same position asalong the a axis at di ff erent temperatures. However, the over-all reflectivity is a little bit lower along the c axis, which isabsolutely reasonable because the conductivity along this di-rection is supposed to be lower. Moreover, the phonon signalsshown in Figure 2 (a) and (b) are quite distinct, revealing dif-ferent oscillating modes. In the following paragraphes, wewill only discuss the characteristic features along the a axis.Basically, the spectra at higher energies are dominated byinterband transitions, as shown in Fig. 2 (c). The peaks cen-tered around 2700 cm − , 4500 cm − and 7800 cm − representfor di ff erent transitions. Remarkably, the interband transitionsexhibit temperature dependence. This is seen more clearlyfor the second peak. As temperature decreases, the peak fre-quency moves to higher energy and its spectral weight is en-hanced simultaneously. The enhancement is linked to the re-duction of Drude spectral weight. As we shall explain below,it may be caused by the shift of chemical potential associatedwith temperature-induced subtle crystal structural change. (a)
300 K 200 K 150 K 80 K 50 K 8 K ( - c m - ) (cm -1 ) p T (K) p ( c m - ) ( c m - ) ( - c m - ) (cm -1 )
300 K 200 K 150 K 80 K 50 K 8 K (b)
FIG. 3: The optical conductivity at di ff erent temperatures up to (a)300 cm − and (b) 10 000 cm − . The short dashed lines are low fre-quency extrapolations by the Hagen-Rubens relation. The inset ofthe upper panel shows the temperature dependent evolution of theplasma frequency ω p and scattering rate of free carriers γ by blacksolid squares and blue open squares respectively. The real part of optical conductivities σ ( ω ) are derivedfrom R( ω ) though Kramers-Kronig relation, as displayed inFigure 3. The Hagen-Rubens relation was used for the lowfrequency extrapolation, and the x-ray atomic scattering func-tions were used in the high frequency extrapolation [30]. Fig-ure 3 (a) shows σ ( ω ) in the low frequency. Although thescreened plasma edge can be clearly observed in R( ω ), theDrude component in σ ( ω ) appears mainly in the extrapolatedregion. Apparently, the Drude spectral weight reduces signif-icantly at low temperature, being consistent with the dramaticshift of plasma edge towards low frequency in R( ω ). In ad-dition, three sharp phonon peaks are resolved at 46, 86 and185 cm − , respectively. When the temperature decreases, thephonon frequencies shift slightly towards higher energies.The free carrier contributions could be quantitatively es-timated from the application of Drude model, which has apeak centered at zero frequency and the peak width is just thecarrier scattering rate γ . The Drude spectral weight, whichgives the plasma frequency ω p = √ π n / m ∗ , could be alter-natively obtained from integrating the low frequency spectralweight by ω p = R ω c σ d ω , where ω c is the cut o ff fre-quency. The integration should sum up all the free carrier contributions, without the influence of any interband transi-tions. We chose the frequency where σ ( ω ) reaches a mini-mum as ω c , which was identified to be 30, 30, 70, 130, 220and 330 cm − in sequence corresponding to increasing tem-peratures. The yielded temperature dependent scattering rateand plasma frequency are plotted in the inset of 3 (a). Thescattering rate decreases from 40 cm − at 300 K to 4 cm − at8K. Meanwhile, ω p drops monotonically upon cooling from1400 cm − to 300 cm − . Assuming the e ff ective mass of freecarriers remains unchanged, then 95% of the population is re-duced. The dramatic reduction of free carriers could hardlybeen explained by reduced thermal excitations. Here, we pro-pose that this peculiar phenomenon is related to the chemicalpotential, which moves closer to the Dirac node as tempera-ture decreasing, along with the lattice shrinking. Theoreticalcalculation suggested that the electronic properties of ZrTe are extraordinarily sensitive to the variation of the lattice pa-rameters [29].Figure 3 (b) presents the optical conductivity in the energyscale up to 10 000 cm − . Corresponding to R( ω ), an excep-tional sharp peak shows up at around 4000 cm − , along witha shoulder-like feature at around 2800 cm − . When tempera-ture decreases, the central frequency of the sharp peak shiftsto higher energy and the half with of it gets smaller. At thelowest temperature, it even becomes quasi-divergence. Thisfeature has never been observed in any other 3D materials.We noticed that the reflectance of single-walled carbon nan-otubes, whose joint density of states (JDOS) are constitutedby individual Van Hove singularities, was reported to showgeometry-dependent resonant peaks [31], which are identifiedto stem from interband transitions between these singularities.Consequently, it is most likely that the quasi-divergent peakexhibited in σ ( ω ) also requires for a Van Hove singularity inthe JDOS of ZrTe , which is rarely seen in a 3D bulk material.Nevertheless, the ZrTe single crystals are easily cleaved bothalong the b and c axis, forming a needle-like compound. Thelattice parameters of a = = = ff ect of a Van Hove singularity.Usually Lorentz model is employed to describe the inter-band transition. However, for present compound, the conduc-tivity data above the Drude component could not be repro-duced by the Lorentz model due to a linear increase of con-ductivity with frequency. To make it clearly to see, the opticalconductivity at 8 K is displayed in Fig. 4, where the linearincreasing is fitted by a red dotted line. Ba´asi and Virosztekshowed that, for a noninteracting electron system consisting oftwo symmetric energy bands touching each other at the Fermilevel whose Hamiltonian depends on the magnitude of the mo-mentum through a power-law behavior, the optical conductiv-ity of the interband contribution has a power-law frequencydependence with σ ( ω ) ∝ ( ~ ω ) d − z , where d is the dimen-sion of the system and z represents for the power-law termof the band dispersion [32]. For example, the two dimen-sional graphene with linear dispersion of ε ( k ) ∝ | k | (that is, d = z =
1) gives rise to a frequency independent conduc- ( - c m - ) (cm -1 ) FIG. 4: The optical conductivity at 8 K below 1200 cm − . The reddotted line are the linear fitting of σ ( ω ) tivity, which has been confirmed by optical experiments [22].For the case of 3D compound ZrTe , the linear rising σ ( ω )demands for d − z =
1. By applying d =
3, a linear dispersion z = Ir O below50 meV [33]. Since pyrochlore iridates were suggested tohost Weyl semimetals [34], the observation has been takenas the evidence of a Weyl semimetal even though the lin-ear increasing only persistd in a very small energy scale.Significantly, several quasicrystals (such as Al . Cu . Fe ,Al . Mn . Si . ) has shown similar behaviors as well [35],all of which are lack of inversion symmetries and were sug-gested to be candidates of Weyl semimetals. Furthermore,3D massless electrons with huge Fermi velocity are certifiedby linear rising optical conductivity in the zinc-blende crys-tal Hg − x Cd x Te, with a proper doping concentration close to x = σ ( ω ) = e h ω v F = G ω v F , where G = e / h = × − Ω − isthe quantum conductance. For ZrTe , band structural calcula-tions indicates only one possible Dirac node near Γ point perZrTe layer [29]. Considering that each Dirac node has a spindegeneracy of 2, we can get the Fermi velocity v F = . × cm / s in terms of the slope of the conductivity shown in Fig.4. This value is significantly smaller than the Fermi velocitydetermined by ARPES experiment along a - or c -axis (smallerbut close to 10 cm / s). We remark that, for 3D Dirac semimet-als, although the linear dispersions exist for all three momen-tum directions, their slopes or Fermi velocities are in fact dif-ferent. ZrTe has a layered structure, the Fermi velocity inthe direction perpendicular to the layers (along b -axis) must be much smaller than the other two directions, unfortunatelypresently available measurement has not yielded such infor-mation. The Fermi velocity determined from optical conduc-tivity for a 3D Dirac semimetal must contain contributionsfrom all momentum directions.For a rigorous Dirac semiemtal, the Fermi energy lies rightacross the Dirac points and the Fermi surfaces would shrinkto isolated points in the BZ. As a result, there would be nofree carriers. The optical conductivity of ZrTe shows obvi-ous Drude component at high temperatures, implying that theFermi energy stays away from the Dirac point. With temper-ature decreasing, the density of free carriers decreases mono-tonically and almost all of them are lost at the lowest temper-ature, which is consistent with the approaching of the Fermilevel to the Dirac point. ARPES measurement has produced avery similar scenario. It is also worth noting that the frequencywhere the conductivity deviates from linear dependence cannot be treated as the cuto ff energy of linear band dispersion,as σ ( ω ) is dramatically modified by other interband transi-tions at higher energies.In conclusion, we have studied the optical conductivity ofthe 3D topological Dirac semimetal material ZeTe . The num-ber of free carriers are proved to be much smaller than con-ventional metals, manifesting a semimetallic behavior. Fur-thermore, it decreases as temperature decreasing, probablycaused by the modification of chemical potential, which mightbe sensitive to the lattice parameter variation. An unexpectedquasi-divergent peak is also observed in the optical conductiv-ity, which is possibly associated with a Van Hove singularityin the JDOS. Most importantly, the optical conductivity growslinearly with frequency below 1200 cm − , presenting the firstoptical spectroscopic evidence of a 3D Dirac semimetal. ACKNOWLEDGMENTS
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