Bulk Fermi surface of the type-II Weyl semimetal candidate NbIrTe 4
Rico Schönemann, Yu-Che Chiu, Wenkai Zheng, Victor Quito, Shouvik Sur, Gregory T. McCandless, Julia Y. Chan, Luis Balicas
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A ug Bulk Fermi surface of the Weyl type-II semimetallic candidate NbIrTe Rico Sch¨onemann, ∗ Yu-Che Chiu,
1, 2
Wenkai Zheng, Victor Quito, Shouvik Sur,
4, 2
Gregory T. McCandless, Julia Y. Chan, and Luis Balicas † National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA Department of Physics, Florida State University, Tallahassee, Florida 32306, USA Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA Department of Chemistry and Biochemistry, The University of Texas at Dallas, Richardson, Texas 75080 USA (Dated: August 2, 2019)Recently, a new group of layered transition-metal tetra-chalcogenides was proposed via first princi-ples calculations to correspond to a new family of Weyl type-II semimetals with promising topologicalproperties in the bulk as well as in the monolayer limit. In this article, we present measurementsof the Shubnikov-de Haas (SdH) and de Haas-van Alphen effects under high magnetic fields for thetype-II Weyl semimetallic candidate NbIrTe . We find that the angular dependence of the observedFermi surface extremal cross-sectional areas agree well with our DFT calculations supporting theexistence of Weyl type-II points in this material. Although we observe a large and non-saturatingmagnetoresistivity in NbIrTe under fields all the way up to 35 T, Hall-effect measurements indicatethat NbIrTe is not a compensated semimetal. The transverse magnetoresistivity displays a four-fold angular dependence akin to the so-called butterfly magnetoresistivity observed in nodal linesemimetals. We conclude that the field and this unconventional angular-dependence are governedby the topography of the Fermi-surface and the resulting anisotropy in effective masses and in carriermobilities. INTRODUCTION
Recently, Weyl fermions have emerged as a heavilystudied subject combining key concepts from high energyand condensed matter physics [1]. In a Weyl semimetal,Weyl fermions emerge around the touching points be-tween linearly dispersing valence and conduction bands.Type-I Weyl points correspond to the “conventional”Weyl Fermions of quantum field theory. Weyl semimet-als require broken inversion or time reversal symmetryfor the Weyl nodes of opposite chirality to separate in k -space or to prevent their pairwise annihilation. Inso-far, several candidates for type-I Weyl semimetals havebeen found, most notably the compounds belonging tothe TaAs family [2–5]. In these compounds angle re-solved photoemission spectroscopy (ARPES) and mag-neto transport experiments were able to reveal a fewcharacteristic signatures of Weyl semimetals like topo-logical Fermi arcs on their surface, the emergence ofa controversial negative longitudinal magnetoresistance(NLMR) when magnetic and electric fields are aligned[6], and the observation of the so-called Weyl-orbits [7].exploring the Fermi arcs.Weyl type-II fermions are predicted to emerge atthe boundary between hole- and electron-pockets result-ing from strongly tilted Weyl cones that break Lorentzinvariance within the crystal and, therefore, have noequivalents in high energy physics [8]. Candidates forWeyl type-II semimetals include non-centrosymmetricmaterials whose inversion symmetry is broken like thelayered orthorhombic transition-metal dichalcogenidesMoTe and WTe [9, 10], as well as MoP and WP [11]which do not crystallize in a layered structure. How- ever, type-II weyl points have been predicted to emergein the ternary tellurides TaIrTe and NbIrTe [12, 13].In fact, the entire family of the M M ′ Te , where M =Ta or Nb and M ′ = Ir or Rh, is candidate for bulk Weyltype-II semimetallic states and is also predicted to dis-play a topological quantum spin hall insulating phase inthe monolayer limit [14]. TaIrTe was the first represen-tative within this family of materials to be claimed toexhibit a Weyl semimetallic state [12]. It was shown thatby including spin-orbit coupling (SOC), TaIrTe hosts aminimum of four Weyl points within the first Brillouinzone. Experimental results from quantum oscillations[15] and ARPES [16, 17] measurements where able toidentify the Weyl points by comparing the measured elec-tronic structure with the DFT calculations. InterestinglyTaIrTe displays a complex electronic structure that canbe tuned by external factors like strain which modifiesthe number of Weyl points or the location of topologicalnodal lines [18].In this article, we investigate the topography of theFermi surface of the Weyl type-II semimetallic candidateNbIrTe via measurements of the de Haas-van Alphen(dHvA) and the Shubnikov-de Haas (SdH) effects to com-pare with band structure calculations. Similar to T d -MoTe and WTe , NbIrTe is a non-centrosymmetriclayered compound belonging to the orthorhombic spacegroup Pmn [19], as shown in Fig. 1 (a). Based onDFT calulations, eight Weyl points emerge within thefirst Brillouin zone in the absence of SOC. After includ-ing SOC a total of 16 Weyl points emerge between thetopmost valence and the lowest conduction band, whichmakes the electronic structure of NbIrTe more complexthan that of its sister compound TaIrTe . These nodesare located within 142 meV of the Fermi energy E F with8 nodes located in the k z = 0 plane and other 8 in k z = ± . METHODS
Single crystals of NbIrTe were grown via a Te fluxmethod. Stoichiometric amounts of elementary Nb(99 . .
99% Sigma Aldrich) withexcess Te were heated in a sealed quartz ampule up to1000 ◦ C and then slowly cooled to 700 ◦ C. After remov-ing the excess Te via centrifugation of the ampoules at700 ◦ C, we obtained shiny metallic crystals with dimen-sions up to 5 × × . . The inset in Fig. 1(b)shows an image of a typical bar-shaped NbIrTe single-crystal. The crystallographic a -axis is in general alignedalong the longest crystal dimension and the c -axis alongthe shortest. The composition and phase purity of oursamples was confirmed by energy-dispersive X-ray spec-troscopy (EDS) and X-ray diffraction. Initial resistiv-ity and Hall-effect measurements on NbIrTe were per-formed in a He-cryostat equipped with a 9 T supercon-ducting magnet (Quantum Design PPMS). Experimentsunder high magnetic fields up to 35 T where performedin resistive Bitter magnets at the National High Mag-netic Field Laboratory (NHMFL) in Tallahassee using He cryostats. AC resistivity measurements were per-formed on single-crystals using the standard 4-wire tech-nique. Additionally, a capacitive cantilever beam tech-nique was used for magnetic torque measurements.In order to obtain the electronic band structure ofNbIrTe and the geometry of its Fermi surface we per-formed DFT calculations including spin-orbit couplingusing the Wien2k package [20]. The Perdew-Burke-Ernzerhof (PBE) exchange correlation functional [21] wasused in combination with a dense k -mesh of 22 × × k -points and a cutoff RK max of 7.5. The structural pa-rameters were taken from Ref. [19]. The angular de-pendence of the SdH and dHvA frequencies, which areassociated to the extremal cross-sectional areas of theFermi surface through the Onsager relation, the effectivecyclotron masses and the charge carrier densities werecalculated using the SKEAF code [22]. For the visual-ization of the crystal structure and of Fermi surface weused the XCrysden [23] package. RESULTS
The layered structure of NbIrTe is displayed in Fig.1(a) and it corresponds to a variant of the WTe oneas discussed in Ref. [19]. Nb and Ir atoms form zigzagchains along the a -direction. When compared to WTe the alternation of Nb and Ir results in a doubling of theunit cell along the b -axis. Measurements of the resistiv- TeIr dc b r ( m W c m ) Nb a H II b H II aH II c H II c r ( m W c m ) T (K)RRR = 17 FIG. 1: (a) Crystallographic structure of NbIrTe . Te atomsare depicted as golden spheres while Ir and Nb atoms arerepresented by red and green spheres, respectively. (b) Resis-tivity as a function of the temperature for a NbIrTe single-crystal. The inset shows a picture of a typical NbIrTe crystal.(c) and (d) Angular dependence of the resistivity under differ-ent magnetic fields at T = 0 .
35 K. In (c) the field was rotatedwithin the bc -plane of the crystal with the current I k a , 0 ◦ corresponds to µ H k c and 90 ◦ to µ H k b . In panel (d) thefield was rotated within the ac -plane with I k b , 0 ◦ is µ H k c and 90 ◦ is µ H k a . ity ρ in the absence of an external magnetic field revealmetallic behavior with ρ ( T ) saturating at low tempera-tures around a residual resistivity ρ ≃ µ Ωcm (see,Fig. 1(b)). The residual resistivity ratio (RRR) which isdefined here as RRR = ρ (300 K) /ρ reaches a value of17 for this particular sample. However, we consistentlyfound RRR values ranging from 15 to 40 across severalsample batches. Although these RRR values are not par-ticularly high, when compared to other layered transitionmetal chalcogenides like MoTe , the resulting residual re-sistivites are relatively low with the presence of quantumoscillations confirming that these crystals are of relativehigh quality. In this manuscript, we include data from4 NbIrTe single-crystals used for resistivity and torquemeasurements at high fields.The angular dependence of the transverse magnetore-sistivity ρ ( θ ) of NbIrTe for fields rotating within the ac -plane, and for I k b -axis, is shown in Fig. 1(d). ρ ( θ ) istwo-fold symmetric with the additional structure emerg-ing at higher fields resulting from the SdH-effect. Itsminimum is observed for fields parallel to the a -axis, im-plying increased inter-layer scattering and a smaller car- aT = 0.35 K H II a r ( m W c m ) H II cT = 0.35 K ~ H b H II b r ( m W c m ) m H (T) H II c
FIG. 2: (a) Resistivity ρ as a function of the magnetic field µ H for different angles between µ H k c and µ H k a -axis. Black dashed line depicts a power law fit of ρ ( µ H )for µ H k c (red curve). (b) ρ as a function of µ H for dif-ferent field orientations in the bc -plane. Above µ H ∼
10 Tquantum oscillations superimposed onto the magnetoresistivebackground are clearly visible in both panels. rier mobility and larger effective masses for fields alongthis orientation.For fields rotating in the bc -plane, as in shown inFig. 1(c), ρ ( θ ) displays a significantly smaller anisotropy,when compared to fields rotating in the ac -plane, reach-ing its maximum for θ ≈ ◦ and its minimum for H k b .This anisotropy results in a four-fold symmetric “but-terfly” shaped angular dependence that is only presentunder magnetic fields exceeding µ H = 10 T . Undersmaller fields the butterfly disappears and ρ ( θ ) becomesmaximal for H k c . This butterfly shaped magnetoresis-tance was also observed in the high- T c superconductors[24], in magnetic thin films, as well as in the Dirac nodalline semimetal ZrSiS [25]. In the case of ZrSiS this be-havior was ascribed to a topological phase-transition as afunction of field orientation that is inherent to the nodalDirac line [25] although the SOC should gap the nodallines that are located in close proximity to its Fermi levelgiven that they are associated to symmorphism.Similarly to TaIrTe [15], the negative longitudinalmagnetoresistance (NLMR) observed in the Weyl type-I monopnictide semimetals [6, 26, 27], which was ascribedto the axial anomaly between Weyl points, is absent inNbIrTe for fields and currents along the a -axis. For Weyltype-II semimetals the positive longitudinal magneto-conductivity observed in Weyl type-I was originally pre-dicted to depend on the orientation of the external mag-netic field relative to wave-vector connecting the Weylnodes [8, 28]. Although, more recently it was claimed tobe orientation independent [29]. In NbIrTe , as well asin TaIrTe , perhaps the Weyl nodes are located too faraway from the Fermi level to lead to charge carriers hav-ing a well-defined chirality or perhaps that their electricaltransport properties are dominated by the topologicallytrivial bands.Figure 2 displays the magneto-resistivity ρ ( µ H ) as afunction of the angle θ for fields rotating within the ac and the bc planes. For µ H k c -axis SdH oscillations,superimposed onto the magnetoresistive background, be-come observable when the field exceeds µ H ∼ a -direction, limiting the observation of quantum os-cillations to θ . ◦ with respect to the c -axis. For ro-tations within the bc -plane the SdH oscillations are vis-ible over the entire angular range. Remarkably, over adecade in field the magnetoresistivity can be fit to a sin-gle power law where ρ ( µ H ) ∝ H α yielding α = 1 . α ≃ . [15]. The first step to address thisbehavior would be to develop a model within Boltzmanntransport theory combining both closed and open orbits,given the geometry of the Fermi surface derived from thecalculations which, as shown below, is confirmed by ourexperiments, including anisotropic effective masses. Asdiscussed by Ref. [31], such approach is capable of de-scribing non-saturating magnetoresistivity displaying anunconventional power dependence on field in addition toreplicating its anisotropy. If conventional transport the-ory was unable to capture this behavior in a scenariothat includes the lack of carrier compensation, one couldconjecture that it might bear relation to the existenceunconventional quasiparticles.In order to reveal the topography of the Fermi surfaceof NbIrTe , we performed magneto-resistivity measure-ments as a function of the angle θ to extract the angu-lar dependence of the SdH frequencies. The results aresummarized in Fig. 3, see also Fig. S3 in SI [30]. Toobtain the oscillatory signal, we fit the magnetoresistivebackground to a polynomial and subsequently subtract itfrom the experimental curve. The fast Fourier transformof the oscillatory component superimposed onto the re-sistivity and torque data can be found in the SI material [100] [010] [001] [100] F F F F DE F = 0meV k y b bad k z F ( k T ) q (deg) k x ga cDE F = -17meV q (deg) k x k y k z k y FIG. 3: (a) and (b) Angular dependence of the SdH frequencies F ( θ ) for NbIrTe . (a) F ( θ ) for the position of the Fermienergy E F resulting from the DFT calculations. (b) F ( θ ) with E F shifted by −
17 meV. The smaller solid points representthe SdH frequencies obtained from DFT calculations using the Onsager relation. Larger triangles depict the position of thepeaks observed in the Fourier transform of the experimental oscillatory signal superimposed onto the resistivity data. Noticethe better agreement between the experimental data and the frequencies resulting from the shift of the Fermi level. F and F can be assigned to the hole pockets labeled as γ and δ in (c), F and F can be assigned to the electron pockets α and β . (see, Fig. S3). According to the DFT calculations theFermi surface of NbIrTe consists of two pairs of spin-orbit split electron (labeled as γ and δ ) and hole-pockets( α and β ) located near the center of the Brillouin Zone(see, Fig. 3(c)). Three of the four pockets ( α , β , and δ ) are strongly corrugated cylinders aligned along the k z and the k y -directions, respectively. The γ sheet forms ananisotropic “kidney” shaped pocket. As shown in Fig.6, for magnetic fields oriented along the c -axis we canidentify three distinct frequencies F , F and F . Basedon their angular dependence F and F can be assignedto the electron pockets and F to the kidney shapedhole-pocket. Although the lower calculated frequenciesassociated to the hole pockets are not clearly visible inthe experimental data, we can achieve a quite acceptableagreement between calculated and experimental frequen-cies by lowering the Fermi level by −
17 meV. Only thesize of the γ -pocket is overestimated in the calculationsby approximately 30%. From the evolution of the Fermisurface with respect to the position of the Fermi energyit is evident that a shift of the γ pocket does not affectthe Weyl points in NbIrTe since they appear at touchingpoints between the δ and the β pockets. Since the Weyltype-II points result from band crossings not associatedwith the band yielding the γ sheet, one can safely statethat these nodes are not affected by the accurate positionof this band relative to the Fermi level, see band depictedby green line in Fig. S4 within the SI file [30].Further justification for lowering the Fermi level comes from Hall-effect measurements that were performed on amechanically exfoliated sample with a thickness of 20 µ mand lateral dimensions of 1-2 mm. We extract the chargecarrier densities and mobilities of NbIrTe from Hall-effect measurements collected between 5 and 100 K undermagnetic fields up to 9 T ( µ H k c -axis) by simultane-ously fitting the longitudinal magneto-resistivity ρ xx andthe Hall resistivity ρ xy to the two-band model: ρ xx = 1 e ( n h µ h + n e µ e ) + ( n h µ e + n e µ h ) µ h µ e B ( n h µ h + n e µ e ) + ( n h − n e ) µ µ B (1) ρ xy = Be (cid:0) n h µ − n e µ (cid:1) + ( n h − n e ) µ µ B ( n h µ h + n e µ e ) + ( n h − n e ) µ µ B (2)where n e , n h are the electron and hole carrier densitiesand µ e , µ h are the electron and hole carrier mobilities,respectively. In this field interval one obtains a reason-able agreement between the experimental data and thefittings, see Fig. 4(a, b). The mobilities increase as thetemperature is lowered to µ e ≈ . × cm / Vs and µ h ≈ . × cm / Vs at T = 5 K, while the electronand the hole densities vary little within this tempera-ture interval. From the low temperature moblities wecan estimate the classical transport lifetime τ D given bythe Drude model, τ D = µ e / h m ∗ /e = 3 . × − s with µ e / h ≈ . / Vs and an effective mass of m ∗ = 0 . m e .This result is comparable with the quantum lifetime ob-tained from SdH oscillations that is related to the Dingletemperature T D : τ Q = ~ / πk B T D = 2 . × − s. As r xx ( m W c m ) a
100 KT = 5K 50 K5 KT = 100 K50 K cd r xy ( m W c m ) m H (T) b n ( / m ) h e m e / h ( m / V s ) T (K) FIG. 4: (a, b) Longitudinal resistivity ρ xx and Hall resistiv-ity ρ xy for NbIrTe as a function of the magnetic field for T = 5 K, 50 K and 100 K. The red lines are fits of ρ xx and ρ xy to the two band model (see equation 2).(c, d) Electronand hole carrier densities n e / h and carrier mobilities µ e / h asa function of the temperature T . n e / h and µ e / h have beenextracted from simultaneous fits of the Hall-effect and of themagnetoresistivity data to the two-band model shown in Fig. 4(d), µ h is smaller than µ e for fields par-allel to c which can be attributed to open Fermi surfacepockets that result in larger effective masses for the holeorbits when compared to the closed electron orbits.At a temperature of 5 K we obtain n e ≈ . × cm − and n h ≈ . × cm − . Therefore, thedensity of holes exceeds the density of electrons by afactor greater than 2. In contrast, the volumes of theindividual Fermi surface sheets for the unshifted Fermilevel (Fig. 5), would yield nearly equal electron and holedensities, making NbIrTe a compensated semimetal. Asdepicted in Fig. 5 lowering the Fermi level leads to anexpansion of the volume of the hole pockets while shrink-ing the electron pockets without fundamentally changingtheir shape. Thus lowering the Fermi level leads to a -30 -15 0 15 300123 n h / n e DE F (meV) DE F = 0meV-11meV-22 meV+11 meV+22 meV-17 meV FIG. 5: Fermi surface of NbIrTe projected on the k y k z -planefor different Fermi energies. The graph shows the calculated n h /n e ratio as a function of the shift in Fermi energy ∆ E F . reduction in n e and to an increase in n h resulting ina better agreement with the Hall-effect data. Hence,NbIrTe is remarkable for not being carrier compensated,and this is consistent with its modest magnetoresistivity,i.e. ∆ ρ ∼ T s under fields up to µ H = 35 T, while displaying non-saturating magnetore-sistivity.The cyclotron effective mass of a given electronic or-bit can be extracted from the temperature damping fac-tor R T in the Lifshitz-Kosevich formula and is given by: R T = λT / sinh( λT ) where λ = 2 π k B m ∗ / ~ eB , with m ∗ being the cyclotron effective mass. The fast Fouriertransform (FFT) of the oscillatory component superim-posed onto the torque data for µ H nearly parallel to the c -axis is shown in the Fig. 6(a). There are at least threedistinct frequencies, which we label as F , F and F .Each correspond to a distinct extremal cross-sectionalarea of the Fermi surface and belong to a different Fermisurface pocket ( α , β , γ ). To extract m ∗ for each indi-vidual orbit, we fit R T to the temperature dependence ofthe amplitude of the peaks observed in the FFT spectra(Fig. 6(b)). As shown in Table I, m ∗ is anisotropic or de-pends on sample orientation with respect to µ H rangingfrom 0.46 to twice the free electron mass. These valuesare comparable to those extracted for TaIrTe [15]. [100] [010] [001] [100] FFT A m p li t ude ( A r b . U n i t s ) F (kT) a F F F F F d H v A S i gna l ( A r b . U n i t s ) m H (1/T) bc FFT A m p . ( A r b . U n i t s ) T (K) F d -33 meV -22 meV -17 meV -11 meV meV E ff e c t i v e M a ss ( A r b . un i t s ) q (deg) DE F = +11 meV FIG. 6: Effective masses of NbIrTe extracted from quantum oscillations. (a) Fast Fourier Transform (FFT) of the oscillatorycomponent on the torque signal shown in (b) for H k c . Frequencies that can be assigned to individual orbits on the Fermisurface pockets are labeled as F , F and F . (b) de Haas-van Alphen oscillations in NbIrTe for temperatures between 0 . T = 20 K. (c) FFT amplitude as a function of the temperature for the dHvA frequencies F , F and F . Solid lines representfits to the temperature damping factor R T in the Lifshitz-Kosevich formalism from which we extract the effective masses. (d)Angular dependence of the cyclotron effective mass averaged across all extremal orbits as obtained from the DFT calculations.For the sake of clarity, these curves are shifted with respect to their respective Fermi levels. The curve assigned to ∆ E F = 0corresponds to the unshifted Fermi energy. Arrows indicate maxima in the average effective mass for fields oriented nearlyalong the b - or the c -axis. We argue that this anisotropy in effective masses leads to the butterfly shaped magnetoresistivity.pocket θ ( ◦ ) m ∗ ( m ) F (kT) α
135 0.76 0.178180 ( c ) 0.47 0.148 β
180 ( c ) 0.62 0.289225 1.0 0.341 γ
45 0.46 0.37290 ( b ) 1.7 0.299125 0.55 0.332 δ
45 2.0 0.72990 ( b ) 1.36 0.496TABLE I: Effective masses of NbIrTe for selected SdH anddHvA frequencies. The pockets are labeled as α , β , γ and δ following Figs. (3) and (6). The angle θ represents theorientation of the magnetic field where θ = 0 ◦ = 270 ◦ ≡ µ H k a , 90 ◦ ≡ µ H k b and 180 ◦ ≡ µ H k c , where m ∗ isthe cyclotron effective mass in units of the free electron mass m , and F the SdH/dHvA frequency. As seen in Table I, m ∗ scales with the size of the ex-tremal cross-sectional orbit with the exception of the γ pocket, which shows an enhanced effective mass for H k b . The presence of open orbits for fields alignedaligned along the crystallographic axes, due to the to-pography of the Fermi surface is likely to affect the angu- lar dependence of the magnetoresistance and this mightexplain the butterfly shaped magnetoresistance. As il-lustrated in Fig. 6(d), the calculated average effectivemass is enhanced along high symmetry directions due tothe presence of open orbits but depends on the positionof the Fermi level. For small shifts ranging from -11 to −
22 meV the cyclotron effective mass shows a maximumalong the b and the c axes but a minimum in between.This would result in a lower carrier mobility ν = qτ /m ∗ (where q is the charge of the carrier and τ the averagescattering time) and hence in a smaller magnetoresistiv-ity for fields along the crystallographic b - and the c -axis,when compared to fields oriented in between both axeswhich yield closed cyclotron orbits. SUMMARY
In summary, we found that the geometry of the Fermisurface of NbIrTe obtained from the DFT calculationsand from quantum oscillation measurements are in rathergood agreement, if one considers a small shift in the po-sition of the Fermi energy which does not affect the exis-tence of Weyl type-II nodes. Our overall results supportthe presence of Weyl points in this material although itdisplays rather conventional transport properties. Fur-thermore, our results contrast to our previous studies on T d -MoTe [32] and WP [33], which are also predictedto display a Weyl type-II semimetallic state, but whoseexperimental Fermi surfaces derived from quantum oscil-lations can only be captured by DFT after electron andhole bands are independently displaced towards higherand lower energies, respectively. For both compoundsthis ad-hoc procedure would suppress their Weyl points,in contrast to their robustness in NbIrTe . Both quantumoscillations and Hall-effect measurements indicate thatNbIrTe is not a compensated semimetal and that theunconventional four-fold anisotropy of its angular mag-netoresistivity is governed by the topography of its Fermisurface and related anisotropy in effective masses. Thegood agreement between bulk measurements and bandstructure calculations imply that the electronic proper-ties of NbIrTe , and hence its topological character, arewell-captured by Density Functional Theory calculations.More importantly, since this compound is exfoliable andpredicted by DFT to display a quantum-spin-Hall insu-lator state in the monolayer limit [14], as recently foundfor WTe [34], our conclusions convey that it would beimportant to explore edge conduction and the effect ofa gate voltage in heterostructures containing monolayersof NbIrTe . ACKNOWLEDGMENTS
We thank S. Sur and V. Quito for helpful discussions.This work was supported by DOE-BES through awardde-sc0002613. JYC acknowledge NSF DMR-1700030 forpartial support. The NHMFL is supported by NSFthrough NSF-DMR-1644779 and the State of Florida. ∗ Electronic address: [email protected] † Electronic address: [email protected][1] B. Yan and C. Felser, Annu. Rev. Condens. Matter Phys. , 337 (2017); N. P. Armitage, E. J. Mele, A. Vishwanath,Rev. Mod. Phys. , 015001 (2018).[2] S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee,G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane,C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan,Nat. Commun. , 7373 (2015).[3] S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane,G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez,B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin,S. Jia and M. Z. Hasan, Science , 613-617 (2015).[4] B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao,J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen,Z. Fang, X. Dai, T. Qian, and H. Ding, Phys. Rev. X ,031013 (2015).[5] H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai,Phys. Rev. X , 011029 (2015).[6] X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang,H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai, and G. Chen, Phys. Rev. X , 031023 (2015).[7] P. J. W. Moll, N. L. Nair, T. Helm, A. C. Potter, I.Kimchi, A. Vishwanath, and J. G. Analytis, Nature ,266 (2016).[8] A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer,X. Dai, and B. A. Bernevig, Nature , 495 (2015).[9] Y. Sun, S.-C. Wu, M. N. Ali, C. Felser, and B. Yan, Phys.Rev. B , 161107(R) (2015).[10] Z. Wang, D. Gresch, A. A. Soluyanov, W. Xie, S. Kush-waha, X. Dai, M. Troyer, R. J. Cava, and B. A. Bernevig,Phys. Rev. Lett. , 056805 (2016).[11] G. Aut`es, D. Gresch, M. Troyer, A. A. Soluyanov, andO. V. Yazyev, Phys. Rev. Lett. , 066402 (2016).[12] K. Koepernik, D. Kasinathan, D. V. Efremov, S. Khim,S. Borisenko, B. B¨uchner, and J. van den Brink, Phys.Rev. B , 201101 (2016).[13] L. Li, H.-H. Xie, J.-S. Zhao, X.-X. Liu, J.-B. Deng, X.-R.Hu, and X.-M. Tao, Phys. Rev. B , 024106 (2017).[14] J. Liu, H. Wang, C. Fang, L. Fu, and X. Qian, Nano Lett. , 467 (2017).[15] S. Khim, K. Koepernik, D. V. Efremov, J. Klotz,T. F¨orster, J. Wosnitza, M. I. Sturza, S. Wurmehl,C. Hess, J. van den Brink, and B. B¨uchner, Phys. Rev.B , 165145 (2016).[16] I. Belopolski, P. Yu, D. S. Sanchez, Y. Ishida, T.-R.Chang, S. S. Zhang, S.-Y. Xu, H. Zheng, G. Chang,G. Bian, H.-T. Jeng, T. Kondo, H. Lin, Z. Liu, S. Shin,and M. Z. Hasan, Nat. Commun. , 942 (2017).[17] E. Haubold, K. Koepernik, D. Efremov, S. Khim, A. Fe-dorov, Y. Kushnirenko, J. van den Brink, S. Wurmehl,B. B¨uchner, T. K. Kim, M. Hoesch, K. Sumida,K. Taguchi, T. Yoshikawa, A. Kimura, T. Okuda, andS. V. Borisenko, Phys. Rev. B , 241108(R) (2017).[18] X. Zhou, Q. Liu, Q. S. Wu, T. Nummy, H. Li, J. Grif-fith, S. Parham, J. Waugh, E. Emmanouilidou, B. Shen,O. V. Yazyev, N. Ni, and D. Dessau, Phys. Rev. B ,241102(R) (2018).[19] A. Mar, S. Jobic, and J. A. Ibers, J. Am. Chem. Soc. , 8963 (1992).[20] P. Blaha, K. Schwarz, P. Sorantin, and S. Trickey, Com-put. Phys. Commun. , 399 (1990).[21] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996).[22] P. Rourke and S. Julian, Comput. Phys. Commun. ,324 (2012).[23] A. Kokalj, J. Mol. Graph. , 176 (1999).[24] V. P. Jovanovi´c, L. Fruchter, Z. Z. Li, and H. Raffy, Phys.Rev. B , 134520 (2010).[25] M. N. Ali, L. M. Schoop, C. Garg, J. M. Lippmann,E. Lara, B. Lotsch, and S. S. P. Parkin, Sci. Adv. ,1601742 (2016).[26] J. Hu, J. Y. Liu, D. Graf, S. M. A. Radmanesh, D. J.Adams, A. Chuang, Y. Wang, I. Chiorescu, J. Wei,L. Spinu, and Z. Q. Mao, Sci. Rep. (UK) , 18674 (2016).[27] F. Arnold, C. Shekhar, S.-C. Wu, Y. Sun, R. D. dos Reis,N. Kumar, M. Naumann, M. O. Ajeesh, M. Schmidt,A. G. Grushin, J. H. Bardarson, M. Baenitz, D. Sokolov,H. Borrmann, M. Nicklas, C. Felser, E. Hassinger, andB. Yan, Nat. Commun. , 11615 (2016).[28] M. Udagawa, and E. J. Bergholtz, Phys. Rev. Lett. ,086401 (2016).[29] G. Sharma, P. Goswami, and S. Tewari, Phys. Rev. B , 045112 (2017).[30] See Supplemental Material at http://link.aps.org/supplemental/ for a log-log plotof the magnetoresistivity of NbIrTe , electronic bandstructure along specific k -directions, Fast Fourier trans-form of the quantum oscillatory signal as a function ofthe field orientation, and two-band model fits of themagnetoresistivity and Hall-effect data.[31] S. N. Zhang, Q. S. Wu, Y. Liu and O. V. Yazyev, Phys.Rev. B , 035142 (2019).[32] D. Rhodes, R. Sch¨onemann, N. Aryal, Q. Zhou, Q. R.Zhang, E. Kampert, Y.-C. Chiu, Y. Lai, Y. Shimura,G. T. McCandless, J. Y. Chan, D. W. Paley, J. Lee, A. D. Finke, J. P. C. Ruff, S. Das, E. Manousakis, andL. Balicas, Phys. Rev. B , 165134 (2017).[33] R. Sch¨onemann, N. Aryal, Q. Zhou, Y.-C. Chiu, K.-W. Chen, T. J. Martin, G. T. McCandless, J. Y. Chan,E. Manousakis, and L. Balicas Phys. Rev. B ,121108(R) (2017).[34] S. Wu, V. Fatemi, Q. D. Gibson, K. Watanabe, T.Taniguchi, R. J. Cava, P. Jarillo-Herrero, Science359