Abstract
The topological nodalline semimetal (TNS) is a unique class of materials with a one dimensional line node accompanied by a nearly dispersionless twodimensional surface state. However, a direct observation of the so called drumhead surface state within current nodalline materials is still elusive. Here, using highresolution angleresolved photoemission spectroscopy (ARPES) along with firstprinciples calculations, we report the observation of a topological nodalloop (TNL) in SrAs_{3}, whereas CaAs_{3} exhibits a topologically trivial state. Our data reveal that surface projections of the bulk nodalpoints are connected by clear drumhead surface states in SrAs_{3}. Furthermore, our magnetotransport and magnetization data clearly suggest the presence (absence) of surface states in SrAs_{3} (CaAs_{3}). Notably, the observed topological states in SrAs_{3} are well separated from other bands in the vicinity of the Fermi level. RAs_{3} where R = Ca, Sr, thus, offers a unique opportunity to realize an archetype nodalloop semimetal and establish a platform for obtaining a deeper understanding of the quantum phase transitions.
Introduction
Experimental discoveries of nontrivial topological states in semimetals such as the Dirac^{1,2,3,4}, Weyl^{5,6,7,8}, and nodalline^{9,10,11,12} semimetals have greatly expanded the family of available topological materials beyond topological insulators^{13,14,15,16,17,18}. In the case of the node line/loop semimetals the valence and conduction bands touch along lines/loops in the Brillouin zone and disperse linearly in directions perpendicular to these lines. The density of states at the Fermi energy in an NLS is greater than that of a Dirac or Weyl semimetal, providing a more favorable condition for investigating exotic nontrivial phases and realistic material platforms for developing applications. Note that, the NLSs are not robust against spinorbit coupling or other perturbations and require crystal symmetries for their protection. To date, several structural classes of NLSs such as PbTaSe_{2}^{19}, LaN^{20}, Cu_{3}PdN^{21}, and ZrSiStype^{10,11,22,23,24,25,26,27} materials have been reported with associated space group symmetries that protect the nodalline state. However, the nodalloop states in PbTaSe_{2}^{19}, and Cu_{3}PdN^{21} lie in the vicinity of other metallic bands, LaN requires multiple symmetries for protection, while in the ZrSiXtype systems the topological states lie above the Fermi level. It is highly desirable, therefore, to find materials which require minimum symmetry protections without the presence of other nearby bands that interfere in isolating topological features within the electronic spectrum.
It has been recently shown that timereversal symmetry (TRS) with a center of inversion symmetry (CIS) is sufficient, in principle, to protect a nodalline state^{28,29,30}. APn_{3} (A = Ca, Sr, Ba, Eu; Pn = P, As) family of compounds has been identified as a potential material class to host such a minimal symmetry protected NLS when SOC is excluded^{29,30}. Among these, CaP_{3} and CaAs_{3} are the only members of this series to have a triclinic crystal structure with space group P1, whereas other members including SrAs_{3} crystallize with higher symmetry structures characterized by space group C2/m. Remarkably, in the P1 space group, CIS is the only crystalline symmetry that can protect the topological nodalline states along with TRS^{30}. So that, such a system can aptly work as the material platform of an ideal nodalloop system. However, the experimental verification of this tempting conjecture has not been reported yet. Our studied material RAs_{3} (R = Ca, Sr) could provide not only the nodalloop state but also the topological surface state or drumhead surface states in momentum space connecting nodal points. RAs_{3} thus appears to be a system with an enhanced topological density of states at the Fermi surface, paving the road for the potential discovery of more exotic states.
Here, we report the experimental observation of a topological nodalloop state in the monoclinic system SrAs_{3} and a trivial state in the triclinic system CaAs_{3} in its (010) surface. Utilizing angleresolved photoemission spectroscopy (ARPES), we systematically study the detailed electronic structure of these materials. Our ARPES data and firstprinciples calculations reveal the presence of a topological nodalloop state around the center (Y) of the Brillouin zone (BZ) in SrAs_{3}. Furthermore, we observe a drumhead surface state connecting the nodalpoint projection along the Y direction. Our magnetotransport data show clear signatures of quantum oscillations suggesting the presence of surface states in SrAs_{3}, while CaAs_{3} lacks such oscillations in magnetic fields up to 9 T. Our experimental data are corroborated by our firstprinciples calculations. Interestingly, our calculations suggest that CaAs_{3} undergoes a topological phase transition from TNL to TI when SOC is turned on (also see refs. ^{29,30}). Furthermore, our experimental data reveal that the Fermi surface of CaAs_{3} is formed by a sole band. Therefore, our study could open up a new platform for studying the interplay between various topological phases.
Results
Crystal structure and sample characterizations
The triclinic crystal structure of CaAs_{3} is shown in Fig. 1(a) (upper panel). The center of inversion lies midway between the neighboring Ca atoms. The crystal structure of SrAs_{3} has higher symmetry compared to that of CaAs_{3} (see Fig. 1(a)), hence, SrAs_{3} crystallizes in a simple monoclinic structure with space group C2/m. Therefore, in addition to the center of inversion symmetry, SrAs_{3} has C2 rotational symmetry. The center of inversion symmetry lies midway between two Sr atoms and the twofold rotational symmetry can be readily observed from the primitive monoclinic unit cell as shown in Fig. 1(a) (lower panel). The corresponding bulk Brillouin zone with high symmetry points is shown in the upper panel of Fig. 1(b). An important point to note that the projections of Y and Γ points on the (010) plane are located at the same point of the BZ. Moreover, note that for the (010) hexagonal surface (around Y), one axis is larger than the other two axes. The lower panel of Fig. 1(b) demonstrates the location of a nodalloop centered around the Y point while the spinorbit coupling (SOC) effect is excluded; here a little deviation from the SYT plane is observed for CaAs_{3} (note inplane for SrAs_{3}).
Figure 1(c,d) show the bulk electronic band structure of CaAs_{3} and SrAs_{3}, respectively, calculated along the various high symmetry directions using tight binding (lines) and firstprinciples (dots) techniques considering the spinorbit coupling (SOC) effect. Analyzing the calculations of both materials without SOC, one finds a nodalloop around the Y point of BZ, which is located in the vicinity of the chemical potential (see Supplementary Fig. 2 in see Supplementary Information for additional data and related analysis). An important point to note that the bands are fully gapped as they diverge from the Y points in both directions. The small gap in CaAs_{3} is due to the fact that the nodal points lie slightly away from the high symmetry points. The inclusion of SOC results in opening a negligible gap in SrAs_{3} and an approximately 40 meV gap in CaAs_{3} along the YΓ direction (see Supplementary Information for additional data and related analysis for details of both with and without SOC calculations). The observed instability of the nodalloop phase against the fullygapped topological phase is in concert with the experimental electrical resistivity data of CaAs_{3}, where a crossover from semimetallic to lowtemperature insulating behavior occurs. However, the insulating character is sufficiently weak enough to neglect in SrAr_{3} for both the transport measurements and firstprinciples calculations (see Supplementary Information for additional data and related analysis). Importantly, the exclusion of SOC to observe nodalline or loop states is a wellknown prevalent technique that has played a significant role in realizing previously reported nodalline semimetals such as LaN^{20}, Cu_{3}(Pd,Zn)N^{21}, ZrSiXtype materials^{10,11,25}, etc.
Fermi surface and constant energy contour plots of RAs_{3}
In order to determine the nature of the charge carriers and to unveil the Fermi surface evolution with the binding energy, we present the Fermi surface and constant energy contour plots in Fig. 2 for the (010) surface. The hexagonal Fermi surface (blue dashed line) of SrAs_{3} is observed with 55 eV incident photon energy in Fig. 2(a). As discussed earlier for the (010) surface, our measured Fermi surface Γ refers to Y point. At the center, we clearly observe a circular pocket which is a result of the surface arclike state near the Fermi level, namely the drumhead surface state. Furthermore, we observe six petallike pockets resembling a flower like shape. Moving towards the higher binding energy (170 meV), we observe that the circular pocket almost disappears and the six petals begin to overlap each other creating a complex feature. The oval shape at the corner also evolves into a small pointlike shape. At around 600 meV below the chemical potential, the oval shape and the circular pocket at the zone center completely disappear indicating the electronlike nature of the bands around these points. However, the six flower petalshaped features evolve into a complex flying bat like feature and confirms the holelike nature of these bands. From the bulk band calculations, one can easily speculate that the six petals will form a bigger nodal ring around the drumhead surface state. However, the corner of the Brillouin zone is not well resolved at this photon energy. Therefore, we conduct a Fermi surface mapping at a higher incident energy (100 eV) at the SLS beamline which further confirm the hexagonal nature of the Brillouin zone (BZ) (see Fig. 3(a) and also see Supplementary Information for additional data and related analysis). Figure 2(b) (left) shows the experimental Fermi surface map of CaAs_{3} within a wide momentum window. Unlike SrAs_{3}, we do not observe the electronlike pockets and flower petal shape at the corner and center of the BZ. Each of the hexagons observed represents an individual BZ of CaAs_{3}. In order to figure out the evolution of the Fermi surface contour, we present the constant energy contour plots in Fig. 2(b) (right) and in see Supplementary Information for additional data and related analysis. In these figures, one can clearly see the distorted hexagonal shape of the BZ and holelike nature of the carriers, that is perfectly reproduced by our calculations (see Supplementary Information for additional data and related analysis).
Observation of nodalloop state in SrAs_{3}
In order to determine the nature of the electronic bands associated with the nodalloop near the Fermi level, the photon energy dependent energymomentum dispersion maps are measured (see Figs. 3 and 4 and see Supplementary Information for additional data and related analysis). Figure 3(a) shows the Fermi surface map measured at 100 eV photon energy. The white dashed lines represent the cut directions for the energymomentum dispersion measurements. Figure 3(b) shows the photon energy dependent dispersion maps along the cut 1 direction of SrAs_{3}. Here, we observe the 2D Fermi surface states which correspond to the drumhead surface states at the Γpoint for all the photon energies. The bulk bands below the surface states are not well resolved at the low photon energies, therefore we plot the dispersion map at 100 eV (see Fig. 3(c)). Here, one can clearly observe the bulk bands which provide an explanation for the flying bat like shape in the BZ at higher binding energies. Furthermore, the Dirac point of the nodalloop and the arc along the YΓ direction meet in the vicinity of the Fermi level. Most importantly, the arclike state does not show any notable dichotomy with photon energies, hence, we conclude that it is surface originated (also see Fig. 3(d) for eye guides and see Supplementary Information for additional data and related analysis). This further confirms our observation of the drumhead surface states and the nodalloop state which is in agreement with our firstprinciples calculations (see Fig. 1(d) and refs. ^{29,30}). Next, we present the dispersion maps along the six electron pockets observed at the corner in Fig. 3(e) (cut 2 direction). A massive Dirac like state is observed with a ~0.3 eV gap size.
Observation of trivial elctronic structure in CaAs_{3}
Figure 4 represents the dispersion maps along the various highsymmetry directions of CaAs_{3} (see Fig. 4(a)). We used several photon energies for probing different values of the perpendicular components of the crystal momentum. From the results presented in Fig. 4(b) (see also see Supplementary Information for additional data and related analysis), it is clear that only a single band appears in the vicinity of the chemical potential without any interference from irrelevant bands. Our calculations suggest that the surface states lie within the upper part of the band, which is located slightly below the chemical potential. Such a naturally tuned clean system in the vicinity of the chemical potential is very crucial for transport behavior as well as for applications. To understand the nature of the bands along this high symmetry direction in the (010) plane, we carried out the banddispersion calculations without (see Fig. 4(c)) and with (see Supplementary Information for additional data and related analysis) the inclusion of SOC. The nodalloop (without SOC) and the surface state (with SOC) are found around the Y point along the \({k}_{x}\) momentum plane. Note that \({k}_{x}\) and \({k}_{y}\) are defined here along the x and y directions and are not defined along the vector direction shown in SF. 2(b) (see Supplementary Information for additional data and related analysis). Most interestingly, the projections of the nodal points in the \({k}_{x}\) direction are connected by the surface states. However, the inclusion of SOC opens up a 40 meV gap along this direction and the system undergoes a topological phase transition from TNL to TI. However, a careful photon energy dependent dispersion map study along the expected nodal line direction reveals a small gap (see Fig. 4(b)) in the vicinity of the nodal loop, which nicely agrees with our firstprinciples calculations. To closely look at the surface state in CaAs_{3}, we show a zoomedin view of the experimental dispersion map, and results of calculations performed near the chemical potential by including SOC (see Fig. 4(d,e)). Interestingly, in Fig. 4(d), as expected from theoretical calculations, we do not see the surface state within the top part near the Fermi level but a finite gap is observed. From the photonenergydependent measurements (see SF.5), one can clearly see the bulk nature of the bands. Importantly, the band around Y shows a sharp k_{z}dependency and the upper part of the band completely vanishes above the Fermi level at 80 eV dispersion map (similarly at 110 eV), which indicates the 3D nature of the bands. The presence of the surface state, on the other hand,can be expected at any photon energy, therefore the observation of pure bulk bands negates the possible presence of a Dirac cone with a surface arc in CaAs_{3}. We conclude that our experimentally observed state in CaAs_{3} is topologically trivial in nature. With no other bands near the Fermi level, CaAs_{3} thus provides a unique opportunity to see the evolution from the TNL phase to the TI phase through small doping. Figure 4(e) shows the calculated dispersion map near the Fermi level where one can see the nearly flat surface state connecting the bulk bands. Figure 4(f) represents the measured dispersion map along the k_{y} directions which clearly supports our previous observations. Here, we observe that the band is almost flattened in the k_{y} direction while we find a sharp dispersion along the k_{x} direction. This could further provide a tuning knob to study more exciting exotic states.
Transport and magnetic measurements on SrAs_{3} and CaAs_{3}
In order to look in more detail on the electronic behavior and its impact on transport properties, we have performed the electrical resistivity and magnetoresistivity measurements of SrAs_{3} and CaAs_{3} single crystals. The electrical transport behavior of SrAs_{3} is presented in Fig. 5(a). In zero magnetic field, the compound exhibits semimetallic properties with a weak temperature dependent resistivity of about 1.5 mΩcm and a shallow minimum in \(\rho \)(T) near 60 K, in concert with the literature data^{31,32}. In a magnetic field of 9 T, applied perpendicular to the electric current, the resistivity of SrAs_{3} notably changes. In the region from room temperature down to about 70 K, the compound shows semiconductinglike behavior, while at lower temperatures, a plateau in \(\rho \)(T) is observed, at which the resistivity is ~50 mΩcm, i.e. it is 3000% larger than the magnitude in zero field. Such a distinct influence of the magnetic field on the electrical transport in SrAs_{3} and the presence of the low temperature plateau are characteristic of topological semimetals^{33}. This behavior can be attributed to fieldinduced changes in mobilities and concentrations of electron and hole carriers in a twoband topological material and similar picture was invoked before to explain unusual galvanomagnetic properties of SrAs_{3}, like firstorder longitudinal Hall effect and magnetoresistivity in Hall geometry^{34}. This behavior can support the presence of drumhead surface states in SrAs_{3} as observed in ARPES measurements where the trajectories of the electrons in 2D surface states are easily influenced by magnetic field. A completely different behavior is observed for CaAs_{3} crystals, where the electrical transport measurements show a semiconducting behavior (see Fig. 5(b)). At room temperature, the resistivity is about 37 mΩcm, and with decreasing temperature it increases nonmonotonically, initially in a semimetallic manner, passing through a smeared shallow maximum near 200 K, but then rises sharply below 15 K. The resistivity measured at 2 K is about 260 Ωcm, which is a value nearly four orders of magnitude larger than that at 300 K. The overall shape of \(\rho (T)\) as well as the values of the resistivity are very similar to those reported in the literature^{31,35}. The semiconducting behavior observed in CaAs_{3} agrees with the presence of a small gap close to the Fermi level that has been found by the photoemission studies. The opening of the finite gap and evidence of 3D nature of bands avoids the possibility of Dirac cones, which is consistent with our transport data. As can be inferred from Fig. 5(b), an external magnetic field of 9 T, applied perpendicular to the electric current, hardly affects \(\rho \)(T) of CaAs_{3} above 10 K, yet brings about a more rapid rise of the resistivity at lower temperatures. The latter feature can be attributed to a small increase in the value of the semiconducting energy gap or/and some reduction in the mobility of dominant charge carriers, both effects being driven by the magnetic field.
Figure 5(c) shows the transverse magnetoresistance (MR) of SrAs_{3} measured at different temperatures and a magnetic field up to 9 T. The MR is defined as the change of the electrical resistance under applied magnetic field and can be described by the formula MR = [R(H) − R(0)]/R(0), where R(H) and R(0) stand for resistance with and without magnetic field, respectively. As can be seen, in the case of SrAs_{3}, the MR is positive and nonsaturating up to 9 T for all temperatures measured. At low temperatures, the MR reaches large values exceeding 3200% at 2 K and 9 T. Such a large MR in SrAs_{3} may indicate the presence of surface states in this material^{36}. The overall MR curve at 2 K can be described by the relation MR ∝ H^{n} with n = 1.82. The nearly quadratic field dependence indicates that the system exhibits an almost complete electronhole compensation, as expected from a semiclassical two band model^{36}. At low temperatures and high magnetic field, a signatures of Shubnikov de Haas (SdH) oscillations can be observed. The inset of Fig. 5(c) shows the oscillations versus inverse magnetic field above 6 T at different temperatures and after subtracting the smooth background from the resistivity data (MR ∝ H^{1.82}). The results have been normalized at 9 T to better show the magnitude of resistance change caused by the quantum oscillations. The presence of the quantum oscillations, even at 15 K (and 9 T) not only points to a very good quality of the SrAs_{3} single crystals used in the present studies but also indicates the high mobility and extremely low effective mass of charge carriers supporting the presence of surface states in this material. In contrast to SrAs_{3}, CaAs_{3} shows a relatively small MR. The MR measured at different temperatures below room temperature are shown in Fig. 5(d). At 2 K, the MR reaches a maximum of 90% at a magnetic field of 8 T and then starts to saturate. At higher temperatures, as shown in Fig. 5(d), the MR is decreasing with increasing temperature and the MR values are nonsaturating up to 9 T. Unlike in SrAs_{3}, we do not observe any sign of the SdH oscillations in CaAs_{3}. The inset of Fig. 5(d) shows the residuals at different temperatures after subtracting the background from resistivity data. As it can be seen, no oscillations are present in the magnetic fields of up to 9 T. This clearly shows a difference between these two systems; SrAs_{3} being a topological semimetal and CaAs_{3} being a trivial semiconductor with a narrow gap in the electronic structure, all in good agreement with the photoemission results. The insulating behavior at low temperature and the relatively small and saturating MR at low temperature could be the reason that both SdH and dHvA oscillations are missing in CaAs_{3}. This is in agreement with the ARPES results suggesting that CaAs_{3} is a trivial insulator. Figure 5(e,f) show the field dependences of the magnetization of SrAs_{3} and CaAs_{3}, respectively, measured at various temperatures. As it can be observed from the figures for CaAs_{3}, the linear field dependence measured is a characteristic feature of a typical diamagnetic insulator. In the case of SrAs_{3} a much complex M(H) behavior is observed with a crossover from weak diamagnetic at weak magnetic field to paramagnetic like behavior at ~5 T. In addition, an obvious de Haas van Alphen (dHvA) oscillations are present for SrAs_{3} at low temperatures and high magnetic fields, as were predicted for topological line node semimetals^{37,38}. In nodal line systems, the magnetic susceptibility is composed into the orbital, spin, and spinorbit cross terms, which is caused by the strong spin orbit interactions^{37,38}. In nodal semimetals the spinorbit cross term is directly related to the chiral surface current (and orbital magnetization) induced by the topological surface modes^{37}. In the case of CaAs_{3}, no such effects exist (see Fig. 5f) and the magnetization shows an ordinary diamagnetic behavior expected for trivial insulators. The temperature dependence of the magnetic susceptibility of SrAs_{3} and CaAs_{3} is shown in the insets of Fig. 5(e,f), respectively. Whilst CaAs_{3} exhibits a typical behavior expected for an ordinary diamagnetic insulator, the magnetic susceptibility of SrAs_{3} shows an unusual Tlinear dependence that may be a signature of its topological nature.
Discussions
Although few topological nodal semimetals have been realized experimentally, there is a lack of available pristine model systems hosting a well isolated drumhead surface state. Our systematic spectroscopic study reveals the clear signature of the drumhead surface state in SrAs_{3}, which is further supported by transport measurements as well as the firstprinciple calculations. Similarly, our results show that CaAs_{3} is a topologically trivial material with a clear band gap. Therefore, by appropriate isoelectric doping in CaAs_{3} with Sr, the quantum phase transition from topological nodal line phase to the topological insulator state can be realized in Sr_{x}Ca_{1−x}As_{3} system. As the topological nodal states are expected to locate in the vicinity of the Fermi level, Sr_{x}Ca_{1−x}As_{3} system could provide an ideal platform for transport as well as optical measurements to reveal the topological nodal signatures. By the application of circularly polarized light, one can drive the nodal line phase into a Weyl phase in this system^{39}. Our systematic spectroscopic and transport measurements as well as firstprinciples calculations show that differences in crystal structures, crystallographic symmetry protections, and the SOC strength will lead to substantial differences in the electronic structures.
Methods
Sample growth and characterizations
Single crystals of RAs_{3} were grown by Snself flux technique as described elsewhere^{40}. Chemical composition of the single crystals was checked by energydispersive Xray analysis using a FEI scanning electron microscope equipped with an EDAX Genesis XM4 spectrometer. The average elemental ratios Ca: As and Sr: As obtained in accord with the expected stoichiometry. The crystal structure of the single crystals was examined by Xray diffraction on a KUMA Diffraction KM4 fourcircle diffractometer equipped with a CCD camera, using graphitemonochromatized MoKα radiation. The triclinic CaP_{3}type crystal structure of CaAs_{3}(space group P1, Wyckoff No. 2) and the monoclinic crystal structure of SrAs_{3} (C2/m, #12) were confirmed, with the crystal lattice parameters close to the literature values reported in refs. ^{35,41}. Measurements of the electrical resistivity were carried out in the temperature range from 2 to 300 K in magnetic field up to 9 T employing a Quantum Design PPMS9 platform. Electrical contacts were made of silver wires attached to the rectangularprismshaped samples with silver epoxy. Because of the very low crystallographic symmetry no effort was made to determine the direction of the electric current in respect to the unit cell axes. The electrical resistivity and magnetotransport properties were measured using standard fourprobe technique and magnetic properties were measured using VSM option in PPMS Dynacool9 (Quantum Design) device.
Synchrotron measurements
We performed synchrotronbased ARPES measurements at the surface and interface spectroscopy beamline endstation highresolution photoemission spectroscopy (SISHRPES) located at the Swiss Light Source (SLS) which is equipped with Scienta R4000 hemispherical electron analyzer. Similarly we collected more data at the Advanced Light Source (ALS) beamlines 10.0.1.1 and 4.0.3 which are equipped with Scienta R4000 and R8000 hemispherical electron analyzers, respectively. During the data collection, energy and momentum resolution were set better than 20 meV and 0.2°, respectively. We cleaved the samples in ultra high vacuum (UHV) conditions where pressure were better than 10^{−10} torr. The measurement temperatures were set to be 10–25 K. We did not observed any sign of sample degradation during the measurements.
Theoretical calculations
In order to analyze and interpret the experimental ARPES data, firstprinciples calculations were performed using both the DFT and TB methods. The DFT calculations were made using Vienna abinitio simulation package based on PerdewBurkerErnzerhof(PBE)^{42} type generalized gradient approximation and the projector augmentedwave(PAW)^{43} pseudopotential. The energy cutoff of 400 eV and a 9 × 9 × 9 k mesh were used to calculate the bulk band structure. A real space TB model based on the Wannier function of As p orbitals was built by using WANNIER90^{44} package. The TB model and Green’s function^{45,46} method were employed to calculate the surface band structure and the Fermi surface energy contours.
Data availability
The data that support the findings of this study are available from the corresponding author upon request.
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Acknowledgements
M.N. is supported by the Air Force Office of Scientific Research under Award No. FA95501710415 and the National Science Foundation (NSF) CAREER award DMR1847962. D.K. is supported by the National Science Centre (Poland) under research grant 2015/18/A/ST3/00057. The work at Northeastern University was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences grant number DEFG0207ER46352, and benefited from Northeastern University’s Advanced Scientific Computation Center (ASCC) and the NERSC supercomputing center through DOE grant number DEAC0205CH11231. K.G. acknowledges support from the DOE’s Early Career Research Program. N.P acknowledges support from INL’s LDRD program (19P45019FP). We thank SungKwan Mo and Jonathan Denlinger for beamline assistance at the LBNL. We also thank Nicholas Clark Plumb for beamline assistance at the SLS, PSI.
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M.N. conceived the study; D.K. synthesized the samples and performed the electrical and magnetic transport characterizations; N.P., and K.G. performed the magnetotransport and magnetization measurements; M.M.H. performed the measurements with the help of G.D., K.D., F.K., C.S., S.R., and M.N.; B.W. and A.B. performed the ab initio calculations; M.M.H. and M.N. wrote the manuscript with the input from all authors; M.N. was responsible for the overall research direction, planning, and integration among the different research units.
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Hosen, M.M., Dhakal, G., Wang, B. et al. Experimental observation of drumhead surface states in SrAs_{3}. Sci Rep 10, 2776 (2020). https://doi.org/10.1038/s41598020592002
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DOI: https://doi.org/10.1038/s41598020592002
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