Abstract
Recent debates in the literature over the relationship between topology and Extreme Magnetoresistance (XMR) have drawn attention to the Lanthanum Monopnictide family of binary compounds. Angle resolved photoemission spectroscopy (ARPES) is used to measure the electronic structure of the XMR topological semimetal candidates LaBi, LaSb, and LaAs. The orbital content of the nearE_{ F } states in LaBi and LaSb are extracted using varying photon polarizations and both dominant d and p bands are observed near X. The measured bulk bands are shifted in energy when compared to the results of Density Functional Calculations. This disagreement is minor in LaBi, but large in LaSb and LaAs. The measured bulk band structure of LaBi shows a clear band inversion and puts LaBi in the υ = 1 class of Topological Insulators (or semimetals), as predicted by calculations and consistent with the measured Diraclike surface states. LaSb is on the verge of a band inversion with a lessclear case for any distinctly topological surface states and in disagreement with calculations. Lastly, these same bands in LaAs are clearly noninverted implying its topological triviality and demonstrating a topological phase transition in the Lanthanum monopnictides. Using a wide range of photon energies the true bulk states are cleanly disentangled from the various types of surface states which are present. These surface states exist due to surface projections of bulk states in LaSb and for topological reasons in LaBi.
Introduction
The binary compounds containing a single pnictogen element with La in a rock salt crystal structure have recently drawn attention in the literature for both demonstrating extreme magnetoresistance (XMR) as well as possible topological states and surface Dirac Fermions.^{1,2,3,4,5,6} Here magnetoresistance is defined by the ratio R(H)/R(0), where R is the electrical resistance and H is the applied magnetic field. In transition metal oxides, both Giant and Colossal Magnetoresistance have been observed^{7,8} and implemented in nonvolatile magnetic memory,^{9} as magnetic sensors,^{10} as well as proposed spin valves in spintronics.^{11} XMR is distinct from these wellunderstood phenomena in that it is exhibited in materials where R(0) is small, i.e., good metals.^{12} The effect also spans several classes of materials including Dirac semimetals,^{13,14} Weyl semimetals,^{15,16,17} and layered semimetals.^{18,19,20}
The complete physical description of the mechanism responsible for XMR is currently not understood. Quantum oscillation studies in the partially electronhole compensated LaSb and LaBi have shown that the electrical transport at low temperature and applied magnetic field is dominated by ellipsoidal electron pockets.^{12} Due to the spinorbit coupling in both of these materials, electronic structure calculations predict mixing between the La d orbital and the pnictogen p orbital bands, which compose the pocket.^{2,12} The mixing of these two bands, in turn, creates an orbital composition crossover at E_{ F } on this pocket. The existence of this crossover is found in many of the materials which exhibit XMR.^{12} Furthermore, topological surface states have been suggested as a necessary ingredient for XMR.^{21,22} Several of the materials which demonstrate XMR have been confirmed or predicted to be, topologically nontrivial^{15,16,17,21} indicating, at minimum, a correlation between the two phenomena.
Electronic structure calculations on the Lanthanum Monopnictides indicate that the d and p bands will cross only once along the Γ − X direction and therefore will be inverted at X.^{2} This inversion, along with the existence of inversion and time reversal symmetries in these systems, would result in a nontrivial Z_{2} invariant for the Lanthanum Monopnictides. The same calculations show the degree of band inversion in a given Lanthanum Monopnictide compound is dependent on the pnictogen species present. Furthermore, these results predict that the inversion magnitude decreases with a smaller atomic number, but is present in all compounds in the family except LaN.^{2}
In this report, we present ARPES measurements as well as bulk electronic structure calculations for LaSb, LaBi, and LaAs. Threedimensional mapping of k space is performed and shows good but not complete agreement with the Density Functional electronic structure calculations, with the most important differences concerning the inversion of the bands at the X point, which impacts the topological order of the materials. A full mapping of k_{ z } using ARPES over several Brillouin zones (BZ) shows the presence of several surface effects in the spectra from both LaBi and LaSb, including unique surface states in LaBi. We make a comparative study of the surface states in both materials with a discussion on the topological nature of these surface states. Furthermore, we utilize the selection rules of the photoemission matrix element to directly extract the orbital composition of the electron pockets found in the bulk of these materials. We report a clear band inversion in LaBi, while LaSb is near a band inversion, and LaAs is clearly noninverted.
Previous ARPES studies have been carried out on LaBi and LaSb focusing on their surface states and corresponding topological classification: in LaBi,^{6,21,22} and in LaSb.^{2,21} However, the topological class of these materials is inferred from calculations and the existence of “Diraclike” dispersions in each of these reports. The consensus reached by refs.^{6,21,22} is that LaBi is topologically nontrivial. Ref. ^{4} claims LaSb to be topologically trivial while ref. ^{21} argues that LaSb is nontrivial.
From direct measurement, we show that LaBi has a band inversion, LaSb is on the verge of inversion, and LaAs is noninverted. This demonstrates a topological phase transition within the family of Lanthanum Monopnictides. As for implications to XMR, we note that only LaBi is topologically nontrivial. From these facts, we conclude the possibility that topology is an essential ingredient for XMR is unlikely.
Results
Single crystals of LaBi, LaSb, and LaAs were cleaved insitu along a 100 crystal face. The presence of a surface termination allows for the possibility of surface states which follow the symmetries of the surface Brillouin zone (SBZ), which are distinct from the bulk Brillouin zone. The relationship between the two zones is shown in black (bulk) and blue (surface) in Fig. 1c. Note that when cleaved on the 100 surface, Γ and one of the three bulk X points, X_{3}, is located at k_{} = 0. Therefore, when projected along the k_{⊥} (k_{ z }) direction, they overlap at the same high symmetry point in the SBZ: \(\overline {\mathrm{\Gamma }}\). Similarly, the bulk X_{2} and W points both project to the surface \(\overline M\) point. These projections to the SBZ require an inplane back folding of states in the SBZ relative to bulk states, as will be discussed in more detail later in the paper. These surface states or surface resonances need to be distinguished from topologically induced surface states.
Results of Density Functional calculations for LaBi and LaSb materials are presented in Fig. 1a, showing the bulk Fermi surface to have two hole pockets centered on the Γ point and ellipsoidal electron pockets centered on the X points. These electron pockets have been indicated to dominate the transport signal in quantum oscillation experiments at low temperature and high magnetic field, the same regime of phase space as XMR.^{12}
The experimental Fermi surfaces as captured by our ARPES measurements are very similar to the calculations, as shown in Fig. 1b,d. Starting from the stacked threedimensional bulk Brillouin zones shown in Fig. 1e, we may take inplane experimental cuts (panel B), or we may hold an inplane value such as k_{ y } fixed, and take a “vertical” slice in k_{ z } such as is shown in panel D. The vertical slices in which k_{ z } is varied allow us to accurately select the high symmetry inplane cuts (for example, the cuts of panel B were taken at k_{ z } = 6* (2π/a), equivalent to k_{ z } = 0). Furthermore, these cuts allow us to distinguish between true bulk states, which disperse in k_{ z } and states localized near the surface, which do not. More details of this will be discussed in a later section, including in the Supplementary Materials, which shows the conversion from photon energies to k_{ z } values.
Visible in panel 1B are the “jackshaped” hole pockets on the Fermi surface, centered at the Γ points ((kx, ky, kz) = (0, 0, 6), (0, 2, 6),(2, 0, 6), (2, 2, 6) in units of 2π/a), as well as the many inplane ellipsoidal electron pockets on the Fermi surface at the bulk X_{1} and X_{2} points ((kx, ky, kz) = (0, 1, 6), (1, 0, 6), (1, 2, 6), etc). These are exactly as expected from the bulk calculations. The outofplane ellipsoids are visible at the X_{3} point, i.e.,: (kx, ky, kz) = (1, 1, 6), (1, −1, 6), etc. These inplane momenta correspond to \(\overline {\mathrm{\Gamma }}\) in the SBZ, as do (1,1,6) and (1, −1,6) and a superposition of spectral weight can be seen around the circular crosssection of the ellipsoid at X_{3} from \(\overline {\mathrm{\Gamma }}\), resulting in a faint jackshape. This weight in panel 1B should be considered as originating from the surface which backfolds spectral weight to the smaller SBZ and/or projects weight to surface states and surface resonances, as will be discussed later.
Understanding the orbital character of the bands is a powerful method to determine the topological classification of a material with inversion and time reversal symmetries.^{23,24} Projecting our Density Functional calculations to an atomic orbital basis, we see that for both LaBi and LaSb, the Xpoint ellipsoidal bands near the Fermi energy are composed of both La d orbitals and pnictogen p orbitals, as shown in Fig. 2e. The tips of the ellipsoidal electron pockets are majority composed of d orbitals, while the midsections of the ellipsoids are of a dominant p orbital character. This is consistent with other calculations on the Lanthanum Monopnictides.^{2,12}
We employ polarization dependent ARPES to confirm the orbital character determined by DFT. Applying symmetry arguments to the photoemission matrix element^{25,26} in conjunction with dipole selection rules, allows us to extract the parity and atomic orbital composition of the electronic wavefunction. This is achieved by comparing the photoemission intensity when the perturbing electric field is even versus odd in the plane defined by the Poynting vector of the light and the sample normal.
Figures 2b, c show the ARPES results for different polarizations and experimental geometries, focusing on the ellipsoidal pockets at the X points. To change the relative orientation of the electron pockets to the Poynting vector of the light, we change the photon energy to move between different k_{ z } planes, namely the X_{2} point at k_{ z } = 5(2π/a) (2B and 2C, left panel) and the X_{1} point at k_{ z } = 6(2π/a) (2B and 2C, right panel). This allows us to minimize tilting away from the high symmetry plane of the crystals, keeping the symmetry analysis as pure as possible.
For σ polarized light (Fig. 2b), the central regions of the ellipses are not visible, for either orientation. Via the dipole selection rules, these results imply a lack of inplane p orbitals along the midsection of the ellipse (see Supplementary Materials for more details). The tips of the ellipses give non zero intensity at X_{1}, and very faint intensity at X_{2}. We attribute this faint intensity at X_{2} to be from impure σ polarization due to the nearly 10° tilting of the sample relative to the Poynting vector at this k_{ y } value. These results for the tips of the ellipsoids require a d orbital odd under reflection in the k_{ z }/k_{ x } plane. To determine the specific d orbital we note that crystal symmetry requires each ellipsoidal tip to transform into each other under rotations. The only d orbital consistent with this constraint for an ellipsoidal pocket pointing in the xdirection is d_{ yz } (Fig. 2d).
When using π polarized light (Fig. 2c), a higher intensity signal from the central region of the ellipse is measured, regardless of the relative inplane orientation of the ellipse to the polarization vector (i.e., both left and right plots of panel C). Using dipole selection rules we conclude the p orbitals along the midsection of the ellipse must be out of plane (see Supplementary Materials). This is consistent with our previous conclusion from the σ polarization measurement. Using π polarization at X_{1}, again we see that the zero in intensity at the tip of the ellipse implies that the d orbital there must be odd under reflection in the k_{ z },k_{ x } plane which is consistent with the d_{ yz } orbital.
From these two measurements, subsequent symmetry arguments, and our simulation we can extract the full orbital content of the electron pockets at the X points. For the ellipsoids pointing along the xdirection, the tips of the ellipsoids are composed of La d_{ yz } orbitals while the equators are composed of tangential pnictogen p orbitals as shown in Fig. 2d. A more detailed description of this analysis is given in the Supplementary Materials.
Figure 3 shows a detailed view of the measured dispersions along the high symmetry directions for both materials along with the surface (blue) and bulk (black) Brillouin zones. Panels A (B) and C (D) shows the raw data from the Γ − X and X − W cuts respectively for LaBi (LaSb). The second derivative of the data (panels E and F) is used to highlight the dispersive features of the raw data and is shown overlaid with a trace of the dispersions. Blue dashed lines indicate a dominant p orbital character of the band as determined from the polarizationdependent ARPES experiments of Fig. 2, as well as from orbitalprojections of our DFT calculations. Red dashes indicate a dominant d orbital character, green and yellow dashes indicate different electronic states that arise due to the presence of the crystal surface and will be described in more detail later.
Panels G and H compile the measured band dispersions (dashed lines, reproduced from panels E and F) with calculated dispersions from DFT (solid red and blue lines). The calculated bands we show are nearly identical to the results from other works,^{2,12} and while they have many close similarities to our experimental bulk bands, they also have some clear differences. In particular, we see that many of the calculated pbands from both LaBi and LaSb are shallower in energy and have less dispersion than the experiment, and the calculated d bands are deeper in energy than the experiment. Most important are the energies of the states at the X point, as these determine whether these materials lie in the ν = 1 topological class or not. As shown in Fig. 3g, the actual agreement between experiment and theory for the LaBi bands at the X point is very good, with the d band, at 0.55 eV, underneath the p band, at 0.1 eV, (inverted) by about 450 meV. This 450 meV inversion gap will be seen to host topological Diraclike states at the surface (yellow dashed), which are presumably directly related to this band inversion.
In LaSb, the disagreements between the calculations and the experiments become much more important, as shown in panel H. The bulk bands from the Density Functional calculation (solid) show the d band at 0.5 eV at X to be about 300 meV below the p band at 0.2 eV at X (inverted), the experimental result of this inversion (dashed lines) is approximately 0 ± 50 meV, i.e., it is not clear whether the bulk bands are inverted or not, therefore we describe LaSb as being on the verge of a topological transition. This will be discussed in more detail in Fig. 4 below.
Discussion
Due to the band inversions that are present at the 3 X points, LaBi can be classified as a 3D topological semimetal and should host Diraclike surface states. However, different surface effects can manifest similarly in ARPES. Therefore, it is important to confirm topologically driven origins. We start with a discussion which shows that the type of surface states in LaSb are different from those in LaBi. Later, we discuss the results of LaAs and show it is topologically trivial. This progression between the two classes of \({\Bbb Z}_2\) topology demonstrates a topological phase transition in the Lanthanum monopnictides.
Figure 3c shows clear evidence of a Diraclike dispersion in LaBi centered at the X point (\(\overline M\) point in the SBZ), which is not present in the bulk Density Functional calculations. To prove that this state is, in fact, a topological surface state (TSS) one must demonstrate the correct number of band inversions exist in the bulk band structure in addition to confirming the state in question is localized to the surface. Projecting the bulk density of states of LaBi along the W − X direction to \(\overline M\) in the [001] SBZ, one can see that there will be a 450 meV direct gap in which only a pure surface state can reside. These states exist within the bulk band gap and also do not disperse in k_{ z } (See Supplemental Information) from the top of the cone down to the valence band. Therefore this state must be localized to the surface.
This information, together with the existence of the band inversion, produces the conclusion that this is a TSS, consistent with previous reports.^{21,22} We label these by the yellow dashed lines in Fig. 3e. The bulk conduction band near X (shown with blue dashed lines) is still present in the ARPES data but is overlapped with the TSS at this location in Fig. 3e,g. The superposition of bulk and surface states is confirmed by considering the k_{ z } behavior. In Fig. 1 panel D we show the Fermi surface in the k_{ z }/k_{ x } plane. There is clear periodicity at the X points, indicating bulk states (for a view of the dispersion along the X − W − X direction in k_{ z } see the Supplementary Fig. S2c,d). The existence of the superimposed TSS is made clear in Supplementary Fig. S3 which shows a Dirac cone that is nondispersive in k_{ z } and overlaps with the bulk X point. Note that because the X_{3} point will project to the \(\overline {\mathrm{\Gamma }}\) surface point of the [001] surface, one also should expect a very lowintensity topological surface state there at the same energy, though the matrix element for observing this state is strongly suppressed in our data, which emphasize the states at X_{1}.
In LaSb the states observed in ARPES that are not present in DFT calculations are of a separate nature. The same band inversion found in LaBi along the Γ − X direction is predicted to exist in our own DFT calculations (Shown in Fig. 4). However, there are conflicting DFT^{2,27} and ARPES^{2,21} studies in the literature that claim the existence of, or lack thereof, a TSS in LaSb. Experimental results (Fig. 3f) show that LaSb is very near the critical point of a band inversion at X, however, we observe no obvious TSS. Although Figs. 3b, d appear to show Diraclike states at X, we find that these are instead replica bands of the bulk dispersion backfolded due to the presence of the crystal surface (which has a smaller, and therefore backfolded Brillouin zone compared to the bulk), which are shown as green dashed lines in Fig. 3f. These backfolded states explain all of the “extra” observed spectral features not predicted by bulk DFT calculations (see Supplementary Materials for a more detailed discussion of this backfolding and k_{ z } resolution). The assignment of all bands in LaSb to either bulk or surfacebackfolded bands means there is no evidence of a separate Diraclike topological surface state (TSS) observed in LaSb, in contrast to the case of LaBi which does have the additional TSS.
Compared to LaBi and LaSb, LaAs is the lightest compound of the three materials. Figure 5 shows the ARPES results from LaAs. Panels (B) and (C) show the Γ − X and X − W cuts respectively. The bands of LaAs are clearly noninverted and therefore LaAs belongs to the topologically trivial (ν = 0) class of materials. In Fig. 4, we compile the evidence for the existence of a topological transition in the Lanthanum Monopnictides. The top row shows our density functional calculations for (from left to right) LaBi, LaSb, and LaAs along the Γ − X direction. The calculations show a trend of decreasing magnitude of the La d band inversion over the pnictogen p band as both the lattice constant and spinorbit coupling decrease in the lighter pnictogen species, though the inversion is still present in LaAs in these calculations and others.^{2} However, our measurements (bottom row) show that in moving from LaBi (left) to LaAs (right) in the pnictogen family the bands are already noninverted.
An important consequence of the LaAs measurements is that the bands can be noninverted and still preserve the mass anisotropy and orbital texture of the ellipsoidal electron pockets at X. If the occurrence of XMR in the LaBi and LaSb were due to the topological nontriviality of these compounds and not the orbital crossover on the electron pockets, then LaAs is an ideal test case for determining the role of topology in the mechanism for XMR in the Lanthanum Monopnictides. At this time we are unaware of any studies of ARPES or XMR in the lighter siblings LaP, or LaN.
We have presented ARPES measurements in which we successfully extract the dispersions in LaBi, LaSb, and LaAs. In addition to this, we determine the dominant orbital contributions of the bands in LaBi and LaSb. From our extraction of the orbital character of the near Fermi surface bands and the ARPES dispersions, we show that LaBi has a clear band inversion at X while LaSb appears to be very near a critical point between trivial and nontrivial topological phases, but does not host an obvious TSS. LaAs clearly lies on the other side of this phase transition in the class of trivial topology. For LaSb and LaAs, this differs from both our own DFT calculations and those in the literature. We observe a topological phase transition in the Lanthanum monopnictides which, argues against a clean role of the topology to the XMR effect.
Methods
The ARPES measurements were done at the Surface/Interface Spectroscopy (SIS) beam line at the Swiss Light Source and the ‘I05’ beamline at Diamond Light Source. For both beam lines, a VGScienta R4000 electron analyzer was used. The photon energies used were from 20 to 240 eV with a total experimental resolution between ~20 and ~150 meV over this range. The angular resolution of the electron lens is 0.2°, corresponding to 0.01 Å^{−1} at 120 eV electron kinetic energy. Both beam lines utilize undulators with polarization control. Preparation of the crystals for the ARPES measurement was done in a nitrogenpurged glove box. A pristine sample surface was obtained by cleaving the crystals in situ in a working vacuum better than 5 × 10^{−11} mbar. Proper alignment of the electron analyzer slit to the crystal axes was achieved to a 0.2 degree precision using 6 axis manipulators by performing maps of the electronic dispersion near E_{ F }.
Density functional theory (DFT) with the projectoraugmented wave pseudopotential and the generalized gradient approximation to exchange and correlation of Perdew, Burke and Ernzerhof as implemented in the Vienna ab initio package (VASP) was utilized. The plane wave basis set size reflected in energy cutoff is 500 eV, and the total energy minimization was performed with a tolerance of 10^{−5} eV. Spinorbit coupling is calculated selfconsistently by a perturbation, \(\mathop {\sum}\nolimits_{i,l,m} {\kern 1pt} V_l^{SO}\vec L \cdot \vec S\left {l,m,i} \right\rangle \left\langle {l,m,i} \right\) to the pseudopotential, where \(\left {l,m,i} \right\rangle\) is the angular momentum eigenstate of ith atomic site. The orbital intensity was calculated by projecting the wave functions, \(\psi \left( {\vec k} \right)\), with a planewave expansion on the orbital basis (spherical harmonics) of each atomic site, as written in the following:
where n, \(\vec k\) denote band index and crystal momentum, respectively.
Data availability
All relevant data are available from the authors upon request.
References
 1.
Tafti, F. F., Gibson, Q. D., Kushwaha, S. K., Haldolaarachchige, N. & Cava, R. J. Resistivity plateau and extreme magnetoresistance in LaSb. Nat. Phys. 12, 272–277 (2015).
 2.
Zeng, M. et al. Topological semimetals and topological insulators in rare earth monopnictides. Arxiv 1504.03492. (2015).
 3.
Alidoust, N. et al. A new form of (unexpected) Dirac fermions in the stronglycorrelated cerium monopnictides. arXiv 1604.08571. (2016)..
 4.
Zeng, L. K. et al. Compensated semimetal LaSb with unsaturated magnetoresistance. Phys. Rev. Lett. 117, 127204 (2016).
 5.
Ghimire, N. J., Botana, A. S., Phelan, D., Zheng, H. & Mitchell, J. F. Magnetotransport of single crystalline YSb. J. Phys. Condens. Matter 28, 235601 (2016).
 6.
Wu, Y. et al. Unusual electronic properties of LaBi—a new topological semimetal candidate. Phys. Rev. B 94, 081108 (2016).
 7.
RodriguezMartinez, L. & Attfield, J. Cation disorder and size effects in magnetoresistive manganese oxide perovskites. Phys. Rev. B 54, R15622 (1996).
 8.
Protière, S., Couder, Y., Fort, E. & Boudaoud, A. The selforganization of capillary wave sources. J. Phys. Condens. Matter 17, 45 S3529 (2005).
 9.
Rao, C. N. R. & Cheetham, aK. Giant magnetoresistance in transition metal oxides. Science 272, 369–370 (1996).
 10.
Lenz, J. E. A Review of Magnetic Sensors. Proc. IEEE 78, 973–989 (1990).
 11.
Wolf, A. S. A. et al. Spintronics: a spinbased electronics vision for the future. Science 294, 1488–1495 (2001).
 12.
Tafti, F. F. et al. Temperaturefield phase diagram of extreme magnetoresistance in lanthanum monopnictides. Proc. Natl. Acad. Sci. 12, 272–277 (2016).
 13.
Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd_{3}As_{2}. Nat. Mater. 14, 280–284 (2015).
 14.
Xiong, J. et al. Anomalous conductivity tensor in the Dirac semimetal Na_{3}Bi. Europhys. Lett. 114, 27002 (2015).
 15.
Shekhar, C. et al. Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nat. Phys. 11, 645–649 (2015).
 16.
Huang, X. et al. Observation of the chiralanomalyinduced negative magnetoresistance: In 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015).
 17.
Ghimire, N. J. et al. Magnetotransport of single crystalline NbAs. J. Phys. Condens. Matter 27, 152201 (2015).
 18.
Mun, E. et al. Magnetic field effects on transport properties of PtSn_4. Phys. Rev. B 85, 035135 (2012).
 19.
Wang, K., Graf, D., Li, L., Wang, L. & Petrovic, C. Anisotropic giant magnetoresistance in NbSb_{2}. Sci. Rep. 4, 7328 (2014).
 20.
Zhu, Z. et al. Quantum oscillations, thermoelectric coefficients, and the fermi surface of semimetallic WTe_{2}. Phys. Rev. Lett. 114, 176601 (2015).
 21.
Niu, X. H. et al. Presence of exotic electronic surface states in LaBi and LaSb. Phys. Rev. B 94, 165163 (2016).
 22.
Nayak, J. et al. Multiple Dirac cones at the surface of the topological metal LaBi. Nat. Commun. 8, 13942 (2017).
 23.
Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).
 24.
Teo, J. C. Y., Fu, L. & Kane, C. L. Surface states and topological invariants in threedimensional topological insulators: Application to Bi_{1−x} Sb_{ x }. Phys. Rev. B 78, 045426 (2008).
 25.
Cao, Y. et al. Mapping the orbital wavefunction of the surface states in threedimensional topological insulators. Nat. Phys. 9, 499–504 (2013).
 26.
Zhu, Z. H. et al. Layerbylayer entangled spinorbital texture of the topological surface state in Bi_{2}Se_{3}. Phys. Rev. Lett. 110, 216401 (2013).
 27.
Guo, P. J., Yang, H. C., Zhang, B. J., Liu, K. & Lu, Z. Y. Charge compensation in extremely large magnetoresistance materials LaSb and LaBi revealed by firstprinciples calculations. Phys. Rev. B 93, 235142 (2016).
Acknowledgements
The authors would like to acknowledge funding for this work by the Department of Energy (grant number: DEFG0203ER46066). This work utilized the Janus supercomputer, which is supported by the National Science Foundation (award number CNS0821794) and the University of Colorado Boulder. The Janus supercomputer is a joint effort of the University of Colorado Boulder, the University of Colorado Denver and the National Center for Atmospheric Research. T.J. Nummy would like to acknowledge the NSF GRFP for their support. Department of Energy, grant number: DEFG0203ER46066. National Science Foundation, award number: CNS0821794 (JANUS Supercomputer). National Science Foundation Graduate Research Fellowship Program.
Author information
Affiliations
Contributions
T.J. Nummy performed the ARPES measurements, density functional calculations, data analysis, wrote and edited the manuscript. J.A.W. and Q.L. performed the Density Functional calculations. J.A.W., S.P., H.L., X.Z., N.C.P. all performed ARPES measurements. F.F.T. and H.Y.Y. synthesized the single crystals and edited the manuscript. D.S.D. directed the research and assisted in writing and edited the manuscript.
Corresponding author
Correspondence to Thomas J. Nummy.
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Nummy, T.J., Waugh, J.A., Parham, S.P. et al. Measurement of the atomic orbital composition of the nearfermilevel electronic states in the lanthanum monopnictides LaBi, LaSb, and LaAs. npj Quant Mater 3, 24 (2018). https://doi.org/10.1038/s4153501800943
Received:
Revised:
Accepted:
Published:
Further reading

Magnetotransport and electronic structure of the antiferromagnetic semimetal YbAs
Physical Review B (2020)

Nonsaturating extreme magnetoresistance and large electronic magnetostriction in LuAs
Physical Review Research (2019)

Interplay of magnetism and transport in HoBi
Physical Review B (2018)

Topological phase transition in LaAs under pressure
Physical Review B (2018)