Observation of topological nodal-line fermionic phase in GdSbTe

M. Mofazzel Hosen,1 Gyanendra Dhakal,1 Klauss Dimitri,1 Pablo Maldonado,2 Alex Aperis,2 Firoza

Kabir,1 Peter M. Oppeneer,2 Dariusz Kaczorowski,3 Tomasz Durakiewicz,4, 5 and Madhab Neupane*1

1Department of Physics, University of Central Florida, Orlando, Florida 32816, USA2Department of Physics and Astronomy, Uppsala University, P.O. Box 516, S-75120 Uppsala, Sweden

3Institute of Low Temperature and Structure Research,Polish Academy of Sciences, 50-950 Wroclaw, Poland

4Condensed Matter and Magnet Science Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA5Institute of Physics, Maria Curie - Sklodowska University, 20-031 Lublin, Poland

(Dated: July 18, 2017)

Topological Dirac semimetals with accidental band touching between conduction and valencebands protected by time reversal and inversion symmetry are at the frontier of modern condensedmatter research. Theoretically one can get Weyl and/or nodal-line semimetals by breaking either oneof them. Most of the discovered topological semimetals are nonmagnetic i.e. respect time reversalsymmetry. Here we report the experimental observation of a topological nodal-line semimetallicstate in GdSbTe using angle-resolved photoemission spectroscopy. Our systematic study revealsthe detailed electronic structure of the paramagnetic state of GdSbTe. We observe the presence ofmultiple Fermi surface pockets including a diamond-shape, an elliptical shape, and small circularpockets around the zone center and high symmetry M and X points of the Brillouin zone (BZ),respectively. Furthermore, we observe the presence of a Dirac-like state at the X point of theBZ. Interestingly, our experimental data show a robust Dirac like state both below and above themagnetic transition temperature (TN ∼ 13 K). Having relatively higher transition temperature (TN

∼ 13 K), GdSbTe provides an archetype platform to study the interaction between magnetism andtopological states of matter.

PACS numbers:

The discovery of 3D topological insulator turned outto be enthralling achievement of the last decade [1, 2]. Athree-dimensional (3D) Z2 topological insulator (TI) isdescribed as a crystalline solid that acts as a traditionalinsulator in the bulk but on its surface it has Dirac elec-tron states that may be conducting, gapless, or even spinpolarized [1–5]. The discovery of such a material dates to2007 in a bismuth based compound initiating a dominoeffect in which the discovery of one exotic state led toanother broadening our knowledge of quantum matterand bringing forth an army of researchers focused on thisnovel field [1–5]. Now we have been able to predict a mul-titude of new materials with exotic states from topologi-cal crystalline insulators to topological Kondo insulators,2D quantum spin Hall insulators and even topologicalsuperconductors using tools, such as symmetries. Con-sideration of electronic states protected by time-reversal,crystalline, and particle hole symmetries has led to theprediction of many novel 3D materials, which can supportWeyl, Dirac, and Majorana fermions, and to new types ofinsulators such as topological crystalline insulators andtopological Kondo insulators, topological superconduc-tors, as well as 2D quantum spin Hall insulators withlarge band gaps capable of surviving room-temperaturethermal excitations [4, 6–11]. Recent attention has fo-cused on exploring non-trivial topological behavior inmetals and semimetals without bulk band gaps, whichcan support symmetry protected gapless points in theBrillouin zone [12–24].

Topological materials offer transformational opportu-nities by providing platforms for entirely new classes of

fundamental science studies of quantum matter as well asthe development of new paradigms for the design of de-vices of the future for wide-ranging applications in nextgeneration electronics, communications and energy tech-nologies [1, 2]. It is envisaged that novel quantum ma-terials will render another breakthrough in technologydevelopment. Essentially currently available topologicalmaterials are mostly non-magnetic, while the magnetictopological materials are limited [25–28]. There is an es-pecially urgent need therefore to find new magnetic topo-logical materials so that the unique potential of these ma-terials for fundamental science studies and applicationscan be explored. This new realm may provide us newexotic states which could be helpful to revolutionize thetechnology to new height. This motivates us to studya magnetic material focusing on the topology and mag-netism.

In this report, we present a systematic studies of amagnetic material GdSbTe in order to reveal the topol-ogy and magnetism in this material using angle-resolvedphotoemission spectroscopy (ARPES), transport mea-surements and first-principles calculations. GdSbTe isisostructural with the nodal line semimetal ZrSiS [29, 30].ZrSiS and related compounds have been shown to ex-hibit a diamond shaped Dirac line node as well as four-fold degenerate nodes at the high-symmetric points ofthe Brillouin zone (BZ) [29–41]. GdSbTe has a relativelyhigher magnetic transition temperature TN , and can beaccessed by ARPES and other techniques. Our system-atic electronic structure studies reveal the presence ofmultiple Fermi surface pockets such as a diamond, a cir-

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FIG. 1: Crystal structure and sample characterization of GdSbTe. (a) Tetragonal type crystal structure of GdSbTe. Layers ofSb atoms form a square net around Gd atoms, which are separated by two Te layers. (b) Spectroscopically measured core-levelof GdSbTe. Here, we clearly observed the sharp peaks of Te 4d (∼ 40 eV), Sb 4d (∼ 33 eV) and Gd 4f (∼ 8.5 eV). (c)Temperature dependence of the reciprocal magnetic susceptibility of single-crystalline GdSbTe measured in a magnetic field of0.1 T applied along the crystallographic c-axis. Solid line represents the fit of Curie-Weiss law to the experimental data. Upperinset: low-temperature magnetic susceptibility data. Lower inset: magnetic field variation of the magnetization in GdSbTemeasured at 1.72 K with increasing (full circles) and decreasing (open circles) magnetic field strength. (d) Ab-initio calculatedbulk band structure of GdSbTe along the various high-symmetry directions.

cular and a elliptical shaped pockets around the Γ, X,and M point, respectively, of the Brillouin zone (BZ).Our study shows that GdSbTe system is not only struc-turally but also electronically similar to ZrSiS and re-lated nonsymmorphic Dirac materials. Importantly, weobserved a Dirac like state at the X point in both theparamagnetic and antiferromagnetic states of this mate-rial. Our findings provide a platform for discovering newexotic quantum phases evolved due to the interplay ofmagnetism with the topological phases.

Single crystals of GdSbTe were grown by chemicalvapor transport method using iodine as a transportingagent [42, 43]. The chemical composition of the crystalswas checked by energy-dispersive X-ray analysis usinga FEI scanning electron microscope equipped with anEDAX Genesis XM4 spectrometer. Single crystal X-raydiffraction (XRD) experiment was performed on a Kuma-Diffraction KM4 four-circle diffractometer equipped with

a CCD camera using Mo Kα radiation. The results indi-cated the tetragonal space group P4/nmm (No. 129)with the lattice parameters a = 4.3104(5) and c =9.1233(15) . The XRD scans revealed that the platelet-shaped crystals have their large surface perpendicular tothe crystallographic c-axis. Magnetic measurements wereperformed in the temperature range from 1.72 K to 400K and in external fields up to 5 T using a QuantumDesign MPMS SQUID magnetometer. For this experi-ment a set of several single-crystalline platelets was ori-ented perpendicular to the magnetic field direction (B ‖c-axis). Synchrotron based ARPES measurement wereperformed at Advanced Light Source (ALS) beamline4.0.3 with a Scienta R8000 hemispherical electron ana-lyzer setup. The angular resolution was set to be betterthan 0.2◦. And the energy resolution was set to be betterthan 20 meV. The electronic structure calculations werecarried out using the Vienna Ab-initio Simulation Pack-

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FIG. 2: Fermi surface and constant energy contour plots. (a) Experimentally measured Fermi surface maps at various photonenergies and at different high symmetry directions. Photon energies are noted in the plots. (b) Constant energy contour plotsat various binding energies. Energies are noted in the plots. High symmetry points are indicated in the leftmost plot. All themeasurements were performed at the ALS beamline 4.0.3 at a temperature of 21 K.

age (VASP) [44, 45], and the generalized gradient approx-imation (GGA) used as the DFT exchange-correlationfunctional [46]. Projector augmented-wave pseudopoten-tials [47] were used with an energy cutoff of 500 eV forthe plane-wave basis, which was sufficient to converge thetotal energy for a given k -point sampling. To simulatethe surface effects, we used 1 × 5 × 1 supercell for the(001) surface, with a vacuum thickness larger than 19 A.

We start our discussion by presenting the crystal struc-ture of the GdSbTe. Similar to other ZrSiS type materialsit also crystallizes into a non-centrosymmetric tetragonalcrystal structure with space group P4/nmm. Fig. 1(a)shows the crystal structure of GdSbTe, where the Gd-Tebilayers are sandwiched between the layers of Sb atomsforming a square net. The sample quality is further ex-amined by performing spectroscopic core-level measure-ment (Fig. 1(b)). Sharp peaks of Te 4d (∼ 40 eV), Sb 4d(∼ 33 eV) and Gd 4f (∼ 8.5 eV) are observed which con-firmed the excellent sample quality used for our measure-ments. The black dashed line represents the Fermi level.Fig. 1(c) displays the magnetic properties of GdSbTe.Above 15 K, the magnetic susceptibility, χ(T), obeys aCurie-Weiss law with the effective magnetic moment µeff

= 7.71 µB and the paramagnetic Curie temperature θ=-19 K. The experimental value of µeff is close to thatexpected for a trivalent Gd ion (7.94 µB). The large neg-ative value of θ signals strong antiferromagnetic exchange

interactions. As shown in the upper inset of Fig. 1(c),the compound orders antiferromagnetically at TN = 13K, and undergoes another magnetic phase transition near8 K. At the lowest temperature attained in the presentwork, i.e. T = 1.72 K, the compound bears an antiferro-magnetic state, as signaled by the character of the mag-netization isotherm displayed in the lower inset to Fig.1c. The magnetic field variation of the magnetization,σ(H), exhibits some tiny inflection near 1.5 T, which canbe attributed to a metamagnetic-like phase transition. Instronger fields, σ(H) of GdSbTe shows a feebly upwardbehavior, which indicates that an expected field-inducedferromagnetic arrangement of the gadolinium magneticmoments can be achieved in this compound in magneticfields much stronger than the maximum field of 5 T avail-able in the present study. We performed ab-initio bulkband calculations on this system along the various highsymmetry directions (Fig. 1(d)). Dirac like feature witha small gap is observed at the X point at around 0.2 eVbelow the Fermi energy.

Figure 2(a) shows Fermi surface maps of GdSbTe inits paramagnetic states at various incident photon ener-gies. High symmetry points and energies are noted inthe plots. The overall Fermi surface is similar to pre-viously reported data on ZrSiS-type materials [30, 39].The topological nodal-line states along the M-Γ-M direc-tions form a diamond shaped Fermi pockets around the

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FIG. 3: Dispersion map along the high symmetry directions. (a) ARPES measured dispersion maps along the M-Γ-M directionat various photon energies. Nodal-line is observed to be in the vicinity of the chemical potential. (b) Dispersion maps alongthe high symmetry X-Γ-X direction. (c) Band dispersion along the M-X-M direction. Dirac-like state is observed. Measuredphoton energies are noted in the plots. All the measurements were performed at the ALS beamline 4.0.3 at a temperature of21 K.

center of the BZ. Furthermore, we observe a small cir-cular and a large elliptical shaped Fermi pockets aroundthe X and M points of the BZ, respectively. Fig. 2(b)shows the constant energy contour plots at various bind-ing energies. Moving towards the higher binding energywe observe that the diamond shape gradually evolves intotwo diamonds. At a higher binding energy a small cir-cular pocket like feature evolves along the Γ-X direction.The small pocket is clearly visible at constant energy con-tour plot with binding energy of 770 meV which is in thevicinity of the Dirac point along this direction.

To reveal the nature of the states along the varioushigh symmetry directions, we present dispersion maps inFigure 3. Fig. 3(a) shows the measured dispersion mapsalong the M-Γ-M direction at various photon energies,

where Dirac line node phase has been observed. Fig.3(b) represents the dispersion maps along the X-Γ-X di-rection. To fully understand the nature of the state alongthe X point, we present dispersion maps along the M-X-M high symmetry direction in Fig. 3(c). Photon energiesare noted in the plots. The Dirac like state is observed atthe X point. In the vicinity of the Dirac point two otherbulk bands are observed.

Since the antiferromagnetic (AFM) transition temper-ature is 13 K in this system, it can provide a platform tostudy the effect of magnetism and topology. We presentdispersion maps along the M-X-M direction both belowand above the magnetic transition temperature of thismaterial in Fig. 4. Temperature values are indicated inthe plots. Interestingly, we observe the Dirac like state

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FIG. 4: Temperature dependent measurement of dispersion maps along the M-X-M direction. Measured temperature are notedon the plots. Re 8K indicates the dispersion map after thermal recycle (8K→21K→53K→8K). All the measurements wereperformed at the ALS beamline 4.0.3.

in both paramagnetic and antiferromagnetic phases. Ourthermally recycled dispersion map (8 K→ 21K→ 53K→8K) indicates the robust nature of the Dirac state in GdS-bTe. Although the time reversal symmetry (T) is brokenin magnetic phase, the product of screw C2x and T mightbe responsible for protecting the Dirac state in the AFMphase (see Supplementary Information).

In conclusion, we performed detailed studies of GdS-bTe material using ARPES, transport measurements andfirst-principles calculations. Our studies reveal the topo-logical nodal state in this material and confirm that theoverall electronic structure is similar with ZrSiS-type ma-terials. Most importantly, we observe a Dirac-like statein both below and above the magnetic transition tem-perature which is around 13 K. With a relatively higher

magnetic transition temperature, GdSbTe can be a po-tential material to study the interactions between themagnetism and topology.

M.N. is supported by the start-up fund from Uni-versity of Central Florida. T.D. is supported byNSF IR/D program. D.K. was supported by the Na-tional Science Centre (Poland) under research grant2015/18/A/ST3/00057. We thank Jonathan Denlingerfor beamline assistance at the LBNL.

Correspondence and requests for materials should beaddressed to M.N. (Email: Madhab.Neupane@ucf.edu).

[1] M. Z. Hasan, and C. L. Kane, Colloquium: topologicalinsulators, Rev. Mod. Phys. 82, 3045-3067 (2010).

[2] X.-L. Qi, and S.-C. Zhang, Topological insulators andsuperconductors, Rev. Mod. Phys. 83, 1057 (2011).

[3] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A.Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z.Hasan, Observation of a large-gap topological-insulatorclass with a single Dirac cone on the surface, Nat. Phys.5, 398 (2009).

[4] M. Z. Hasan, S.-Y. Xu, and M. Neupane, TopologicalInsulators: Fundamentals and Perspectives, (John Wileyand Sons, New York, 2015).

[5] M. Neupane, A. Richardella, J. Sanchez-Barriga, S.Y.Xu, N. Alidoust, I. Belopolski, C. Liu, G. Bian, D. Zhang,D. Marchenko, A. Varykhalov, O. Rader, M. Leanders-son, T. Balasubramanian, T.-R. Chang, H.-Tay Jeng, S.Basak, H. Lin, A. Bansil, N. Samarth, and M. Z. Hasan,Observation of quantum-tunnelling-modulated spin tex-ture in ultrathin topological insulator Bi2Se3 films, Nat.Commun. 5, 3841 (2014).

[6] L. Fu, Topological crystalline insulators, Phys. Rev. Lett.106, 106802 (2011).

[7] Q. Xu, Z. Song, S. Nie, H. Weng, Z. Fang, and X. Dai,

Two-dimensional oxide topological insulator with iron-pnictide superconductor LiFeAs structure, Phys. Rev.Lett. 106, 106802 (2011).

[8] M. Neupane, N. Alidoust, S.-Y. Xu, T. Kondo, Y. Ishida,D. J. Kim, C. Liu, I. Belopolski, Y. J. Jo, T-R. Chang, H-T. Jeng, T. Durakiewicz, L. Balicas, H. Lin, A. Bansil,S. Shin, Z. Fisk, and M. Z. Hasan, Surface electronicstructure of the topological Kondo-insulator candidatecorrelated electron system SmB6, Nat. Commun. 4, 2991(2013).

[9] M. Neupane, N. Alidoust, M. M. Hosen, J.-X. Zhu, K.Dimitri, S.-Y. Xu, N. Dhakal, R. Sankar, I. Belopolski, D.S. Sanchez, T.-R. Chang, H.-T. Jeng, K. Miyamoto, T.Okuda, H. Lin, A. Bansil, D. Kaczorowski, F. C. Chou,M. Z. Hasan, and T. Durakiewicz, Observation of thespin-polarized surface state in a noncentrosymmetric su-perconductor BiPd, Nat. Commun. 7, 13315 (2016).

[10] M. Neupane, Y. Ishida, R. Sankar, J.-X. Zhu, D. S.Sanchez, I. Belopolski, S.-Y. Xu, N. Alidoust, M. M. Ho-sen, S. Shin, F. Chou, M. Z. Hasan, and T. Durakiewicz,Electronic structure and relaxation dynamics in a su-perconducting topological material, Sci. Rep. 6, 22557(2016).

6

[11] M. Neupane, S.-Y. Xu, N. Alidoust, G. Bian, D. J. Kim,C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, T. Du-rakiewicz, H. Lin, A. Bansil, Z. Fisk, and M. Z. Hasan,Non-Kondo-like Electronic Structure in the CorrelatedRare-Earth Hexaboride YbB6, Phys. Rev. Lett. 114,016403 (2015).

[12] Z. Wang, H. Weng, Q. Wu, Xi Dai, and Z. Fang, Three-dimensional Dirac semimetal and quantum transport inCd3As2, Phys. Rev. B 88, 125427 (2013).

[13] M. Neupane, S.-Y. Xu, R. Sankar, N. Alidoust, G. Bian,C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin,A. Bansil, F.-C. Chou, and M. Z. Hasan, Observation ofa three-dimensional topological Dirac semimetal phase inhigh-mobility Cd3As2, Nat. Commun. 5, 3786 (2014).

[14] B.-J. Yang, and N. Nagaosa, Classification of sta-ble three-dimensional Dirac semimetals with nontrivialtopology, Nat. Commun. 5, 4898 (2014).

[15] M. Neupane, M. M. Hosen, I. Belopolski, N. Wakeham,K. Dimitri, N. Dhakal, J.-X. Zhu, M. Z. Hasan, E. D.Bauer, and F. Ronning, Observation of Dirac-Like Semi-Metallic Phase in NdSb, J. Phys.: Condens. Mat. 28,23LT02 (2016).

[16] S. M. Young, and C. L. Kane, Dirac Semimetals in TwoDimensions, Phys. Rev. Lett. 115, 126803 (2015).

[17] 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, A WeylFermion semimetal with surface Fermi arcs in the tran-sition metal monopnictide TaAs class, Nat. Commun. 6,7373 (2015).

[18] H. Weng, C. Fang, Z. Fang, B. A. Bernevig, andX. Dai, Weyl Semimetal Phase in Noncentrosymmet-ric Transition-Metal Monophosphides, Phys. Rev. X 5,011029 (2015).

[19] 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, Discovery of a Weyl fermion semimetaland topological Fermi arcs, Science 349, 613 (2015).

[20] 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, Experimental Dis-covery of Weyl Semimetal TaAs, Phys. Rev. X 5, 031013(2015).

[21] I. Belopolski, S.-Y. Xu, D. S. Sanchez, G. Chang, C.Guo, M. Neupane, H. Zheng, C.-C. Lee, S.-M. Huang,G. Bian, N. Alidoust, T.-R. Chang, B. Wang, X. Zhang,A. Bansil, H.-T. Jeng, H. Lin, S. Jia, and M. Z. Hasan,Criteria for Directly Detecting Topological Fermi Arcs inWeyl Semimetals, Phys. Rev. Lett. 116, 066802 (2016).

[22] M. Z. Hasan, S.-Y. Xu, and G. Bian, Topological in-sulators, topological superconductors and Weyl fermionsemimetals: discoveries, perspectives and outlooks, Phys.Scr. T164, 014001 (2015).

[23] R. S. K. Mong, A. M. Essin, and J. E. Moore, Antiferro-magnetic topological insulators, Phys. Rev. B 81, 245209(2010).

[24] P. Tang, Q. Zhou, G. Xu, and S.-c. Zhang, Dirac fermionsin an antiferromagnetic semimetal, Nat. Phys. 12, 1100-1104 (2016).

[25] M. Hirschberger, S. Kushwaha, Z. Wang, Q. Gibson, S.Liang, C. A. Belvin, B. Bernevig, R. J. Cava, and N. Ong,The chiral anomaly and thermopower of Weyl fermions

in the half-Heusler GdPtBi, Nat. Mater. 15, 11611165(2016).

[26] Z. Wang, M. Vergniory, S. Kushwaha, M. Hirschberger,E. Chulkov, A. Ernst, N. Ong, R. J. Cava, and B.A. Bernevig, Time-Reversal-Breaking Weyl Fermions inMagnetic Heusler Alloys, Phys. Rev. Lett. 17, 236401(2016).

[27] S. Borisenko, D. Evtushinsky, Q. Gibson, A. Yaresko, T.Kim, M. Ali, B. Buechner, M. Hoesch, and R. J. Cava,Time-Reversal Symmetry Breaking Type-II Weyl Statein YbMnBi2, arXiv:1507.04847(2015).

[28] L. M. Schoop, A. Topp, J. Lippmann, F. Orlandi, L. Muchler, M. G. Vergniory, Y. Sun, A. W. Rost, V. Duppel,M. Krivenkov, S. Sheoran, P. Manuel, A. Varykhalov, B.Yan, R. K. Kremer, C. R. Ast, and B. V. Lotsch, TunableWeyl and Dirac states in the nonsymmorphic compoundCeSbTe, arXiv:1707.03408v1 (2017).

[29] L. M. Schoop, M. N. Ali, C. Straber, V. Duppel, S.S. P. Parkin, B. V. Lotsch, and C. R. Ast, Diraccone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS, Nat. Commun. 7,11696 (2016).

[30] M. Neupane, I. Belopolski, M. M. Hosen, D. S. Sanchez,R. Sankar, M. Szlawska, S.-Y. Xu, K. Dimitri, N. Dhakal,P. Maldonado, P. M. Oppeneer, D. Kaczorowski, F. C.Chou, M. Z. Hasan, and T. Durakiewicz, Observation ofTopological Nodal Fermion Semimetal Phase in ZrSiS,Phys. Rev. B 93, 201104, (2016).

[31] A. A. Burkov, M. D. Hook, and L. Balents, Topologicalnodal semimetals, Phys. Rev. B 84, 235126 (2011).

[32] M. Phillips, and V. Aji, Tunable line node semimetals,Phys. Rev. B 90, 115111 (2014).

[33] H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai, andY. Kawazoe, Topological node-line semimetal in three-dimensional graphene networks, Phys. Rev. B 92, 045108(2015).

[34] Y. Kim, B. J. Wieder, C. L. Kane, and A. M. Rappe,Dirac Line Nodes in Inversion-Symmetric Crystals, Phys.Rev. Lett. 115, 036806 (2015).

[35] L. S. Xie, L. M. Schoop, E. M. Seibel, Q. D. Gibson, W.Xie, and R. J. Cava., A new form of Ca3P2 with a ringof Dirac nodes, Appl. Phys. Lett. Mat. 3, 083602 (2015).

[36] J. Hu, Z. Tang, J. Liu, X. Liu, Y. Zhu, D. Graf, Y.Shi, S. Che, C. N. Lau, J. Wei, and Z. Mao, Evidenceof topological nodal-line fermions in ZrSiSe and ZrSiTe,Phys. Rev. Lett. 117, 016602 (2016).

[37] D. Takane, Z. Wang, S. Souma, K. Nakayama, C. X.Trang, T. Sato, T. Takahashi, and Y. Ando, Dirac-nodearc in the topological line-node semimetal HfSiS, Phys.Rev. B 94, 121108(R) (2016).

[38] J. Hu, Y.L. Zhu, D. Graf, Z.J. Tang, J.Y. Liu, andZ.Q. Mao, Quantum oscillation studies of topologicalsemimetal candidate ZrGeM (M=S, Se, Te), Phys. Rev.B 95, 205134 (2017).

[39] M. M. Hosen, K. Dimitri, I. Belopolski, P. Maldonado,R. Sankar, N. Dhakal, G. Dhakal, T. Cole, P. M. Op-peneer, D. Kaczorowski, F. C. Chou, M. Z. Hasan, T.Durakiewicz, and M. Neupane, Tunability of the topolog-ical nodal-line semimetal phase in ZrSiX-type materials,Phys. Rev. B 95, 161101 (2017).

[40] A. Topp, J. M. Lippmann, A. Varykhalov,V. Duppel,B. V. Lotsch, C. R. Ast, and L. M. Schoop, Non-symmorphic band degeneracy at the Fermi level in Zr-SiTe, New J. Phys. 18, 125014 (2016).

7

[41] C. Chen, X. Xu, J. Jiang, S. -C. Wu, Y. P. Qi, L. X. Yang,M. X. Wang, Y. Sun, N.B.M. Schrter, H. F. Yang, L. M.Schoop, Y. Y. Lv, J. Zhou, Y. B. Chen, S. H. Yao, M.H. Lu, Y. F. Chen, C. Felser, B. H. Yan, Z. K. Liu, andY. L. Chen, Dirac Line-nodes and Effect of Spin-orbitCoupling in Non-symmorphic Critical Semimetal MSiS(M=Hf, Zr), Rev. B 95, 125126 (2017).

[42] C. Wang, and T. Hughbanks, Main Group Element Sizeand Substitution Effects on the Structural Dimension-ality of Zirconium Tellurides of the ZrSiS Type, Inorg.Chem. 34, 5524-5529 (1995).

[43] R. Singha, A. Pariari, B. Satpati, and P. Mandal, Titanicmagnetoresistance and signature of non-degenerate Diracnodes in ZrSiS, arXiv:1602.01993v1 (2016).

[44] G. Kresse, and J. Furthmuller, Efficient iterative schemesfor ab initio totalenergy calculations using a plane-wavebasis set, Phys. Rev. B. 54, 11169 (1996).

[45] G. Kresse, and J. Hafner, Ab initio molecular dynamicsfor open-shell transition metals, Phys. Rev. B 48, 13115(1993).

[46] G. Kresse, and D. Joubert, From ultrasoft pseudopo-tentials to the projector augmented-wave method, Phys.Rev. B 59, 1758 (1999).

[47] J. P. Perdew, K. Burke, and M. Ernzerhof, GeneralizedGradient Approximation Made Simple, Phys. Rev. Lett.77, 3865 (1996).