Abstract
The Kondo insulator SmB_{6} has long been known to exhibit lowtemperature transport anomalies whose origin is of great interest. Here we uniquely access the surface electronic structure of the anomalous transport regime by combining stateoftheart laser and synchrotronbased angleresolved photoemission techniques. We observe clear ingap states (up to ~4 meV), whose temperature dependence is contingent on the Kondo gap formation. In addition, our observed ingap Fermi surface oddness tied with the Kramers’ point topology, their coexistence with the twodimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, taken together, collectively provide strong evidence for protected surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological Fermi surface. Our observations of systematic surface electronic structure provide the fundamental electronic parameters for the anomalous Kondo ground state of correlated electron material SmB_{6}.
Introduction
Materials with strong electron correlations often exhibit exotic ground states such as the heavy fermion behaviour, Mott or Kondo insulation and unconventional superconductivity. Kondo insulators are mostly realized in the rareEarthbased compounds featuring felectron degrees of freedom, which behave like a correlated metal at high temperatures, whereas a bulk bandgap opens at low temperatures through the hybridization^{1,2,3} of nearly localizedflat f bands with the dderived dispersive conduction band. With the advent of topological insulators^{4,5,6,7,8,9} the compound SmB_{6}, often categorized as a heavy fermion semiconductor^{1,2,3}, attracted much attention due to the proposal that it may possibly host a topological Kondo insulator phase (TKI) at low temperatures where transport is anomalous^{10,11,12}. The anomalous residual conductivity is believed to be associated with electronic states that lie within the Kondo gap^{13,14,15,16,17,18,19,20,21,22}. To this date no angleresolved photoemission spectroscopy (ARPES) has been used to gain insights on the surface electronic structure of this compound in this anomalous transport regime with appropriately matched required energy resolution and d/f orbital contrast selectivity. Following the prediction of a TKI phase, there have been several transport measurements that include observation of a threedimensional (3D) to twodimensional (2D) crossover of the transport carriers below T~7 K (which fully saturates around 5 K) and clear signatures of a coherent Kondo lattice hybridization onset around 30 K^{23,24,25}, suggesting three regimes of the transport behaviour^{24,25}. First, weakly interacting and singleion resonance regime covering 30–150 K or higher; second, a 3D transport regime in the Kondo lattice hybridization regime covering a temperature range of 8–30 K; third, a 2D anomalous transport regime (6 K or lower), which is the ground state (T~0) of this compound. However, to this date, no temperaturedependent study of the lowenergy states that are predicted to lie within 5 meV exist that provide the momentumresolved nature of the lowlying bands and their Fermi surface character in this system. Despite many transport results available so far, a number of issues critically important for determining the relevance to the Z_{2} topological bandtheory of the groundstate band structure are not known. These include a direct knowledge of the following: first, topology or connectivity of the Fermi surface that is responsible for the apparently highly conducting 2D transport^{23,24,25}; second, the ingap states that give rise to the Fermi surface must be temperature dependent and vanish below the coherent Kondo lattice hybridization scale of 30 K^{25} if they are related to the topology; third, for the observed 2D transport to be of topological origin, it must be due to odd number of pockets, which is not known from transport; fourth, Fermi pockets must enclose only an odd number of Kramers’ points of the Brillouin zone (BZ) lattice that relate to the bulk band inversion but not any other high symmetry point; and fifth, the surface should exhibit nontrivial Berry’s phase as a consequence^{6} of the facts mentioned in the first to fourth, since these conditions are the TKI equivalents of the topological band insulators^{6,10,11,12} (also see Supplementary Discussion and Supplementary Figs S1–S5). Since there are three distinct transport regimes, the true ground state lies only at the anomalous transport regime. Previous ARPES studies were not only limited to temperatures outside this interesting regime (typically higher than 10–20 K)^{16,17} but also missed to identify features within 5 meV and their kspace maps due to a limited combined resolution, namely, the condition of ‘better than 5 meV and 7 K temperature combination’. By combining highresolution laser and synchrotronbased angleresolved photoemission techniques, we uniquely access the surface electronic structure on the samples (growth batch) where transport anomalies were identified^{23,24}. We identify the ingap states that are strongly temperature dependent and disappear before approaching the coherent Kondo hybridization scale. Our Fermi surface mapping covering the lowenergy part of the ingap states only, yet having the sample lie within the transport anomaly regime reveals an odd number of pockets that enclose three out of the four Kramers’ points of the surface BZ. This is remarkably consistent with the theoretical prediction for a topological surface Fermi surface in SmB_{6} by Lu et al.^{12} Our observed Fermi surface oddness, Kramers’ point windingonly topology of the ingap states, their direct correlation with the 2D transport anomaly and their coexistence with the robust Kondo lattice hybridization, as well as their robustness against thermal recycling all taken together by far provide the strongest evidence for the surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological surface Fermi surface of a Kondo insulator. The laser and synchrotronbased bulk and surface band identifications of the lowtemperature phase by themselves collectively provide the fundamental quantitative electronic parameters for the anomalous ground state band structure of SmB_{6}.
Results
Crystal structure and transport anomaly
SmB_{6} crystallizes in the CsCltype structure with the Sm ions and the B_{6} octahedra being located at the corner and at the body centre of the cubic lattice, respectively (see Fig. 1a). The bulk BZ is a cube made up of six square faces. The centre of the cube is the Γ point, whereas the centres of the square faces are the X points. Because of the inversion symmetry of the crystal, each X point and its diametrically opposite partner are completely equivalent. Therefore, there exist three distinct X points in the BZ, labelled as X_{1}, X_{2} and X_{3}. It is well established that the lowenergy physics in SmB_{6} is constituted of the nondispersive Sm 4f band and the dispersive Sm 5d band located near the X points^{16,17,23,24,25}. To crosscheck the established properties, we present the temperaturedependent resistivity profile as well as the overall electronic band structure (Fig. 1c–e) for samples used in our ARPES measurements. The resistivity profile shows a rise for temperatures below 30 K, which is in agreement with the opening of the Kondo gap at the chemical potential. Thus, the Fermi level in our sample lies within the bandgap and sample is bulk insulating. Moreover, at T≤6 K, the resistivity starts/begins to saturate (which fully saturates below 5 K, Fig. 1), indicating the onset of 2D transport anomaly^{13,15}.
Bulk band structure
In Fig. 1d,e, we present ARPES intensity profiles over a wide binding energy scale measured with a synchrotronbased ARPES system using a photon energy of 26 eV. The nondispersive Sm 4f states near the Fermi level are seen and clearly identified in the integrated energy distribution curves. The location of the flat bands are estimated to be at binding energies of 15 meV, 150 meV and 1 eV, which correspond to the ^{6}H_{5/2}, ^{6}H_{7/2} and ^{6}F multiplets of the Sm^{2+} (f^{6}–f^{5}) final states, respectively, in agreement with the earlier reports^{16,17} (see also Supplementary Discussion and Supplementary Fig. S6). The dispersive features we observe originate from the Sm 5dderived bands and a hybridization between the Sm 5d band and Sm 4f flat band is visible especially around 150 meV binding energies confirming the Kondo ingredients of the electronic system in our study (Fig. 1d,e).
Ingap states and Fermi surface
To search for the predicted ingap states within 5 meV of the Fermi level, we employ a laserbased ARPES system providing ΔE~4 meV coupled with a lowtemperature (T5 K) capability. This combination allows us to study the transport anomaly regime with appropriate energy resolution. Furthermore, the choice of 7 eV photons from a laser source is due to the fact that it allows us to improve the relative photoionization crosssection for the d/f content of the hybridized band. At 7 eV, the crosssection for the f orbitals is weaker than it is at typical synchrotron photon energies^{26}, so the measured states have better correspondence to the partial dorbital character of the hybridized band, which is favourable for isolating the topological surface states^{10,11,12}. This is further important for the identification of the ingap states at all Kramers’ points and systematically probing their simultaneous or coupled temperature evolution (if any) as well as measuring their kspace maps. At higher photon frequencies as in the case of synchrotronbased ARPES detections, the felectron contribution can be quite large, thus masking out the lowenergy 2D states due to the f component of the strong band tails. The current study thus focuses on testing the proposal of kspace maps of ingap states and their connection with the 2D transport regime by optimizing the best possible scenarios along the line of specific requirements of the theoretical predictions in refs 10, 11, 12.
Since the lowenergy physics including the Kondo hybridization process occurs near the three X points (Fig. 2a) in the bulk BZ and the X points project onto the , and the points at (001) surface (Fig. 1b), the Kramers’ points of this lattice are , , and , and we need to systematically study the connectivity (winding) of the ingap states around these points. In Fig. 2c, we show our measured ARPES spectral intensity integrated in a narrow (±0.15 Å^{−1}) momentum window and their temperature evolution around the point. At temperatures above the hybridization scale, only one spectral intensity feature is observed around E_{B}~12 meV in the ARPES energy distribution curve profile. As temperature decreases below 30 K, this feature is found to move to deeper binding energies away from the chemical potential, consistent with the opening of the Kondo hybridization gap while Fermi level is in the insulating gap (bulk is insulating, according to transport, so Fermi level must lie ingap at 6 K). At lower temperatures, the gap value of hybridized states at this momentum space regime is estimated to be about 16 meV. More importantly, at a low temperature T6 K corresponding to the 2D transport regime, a second spectral intensity feature is observed at the binding energy of E_{B}~4 meV, which lies inside the insulating gap. Our data thus experimentally show the existence of ingap states. Remarkably, the ingap state feature is most pronounced at low temperature T6 K in the 2D transport regime, but becomes suppressed and eventually vanishes as temperature is raised before reaching the onset for the Kondo lattice hybridization at 30 K. The ingap states are found to be robust against thermal cycling, since lowering the temperature back down to 6 K results in the similar spectra with the reappearance of the ingap state features (Re_6 K in Fig. 2c). Within a 30h period, we did not observe any significant aging effect in our samples while maintaining an ultrahigh vacuum level better than 4 × 10^{−11} Torr. The observed robustness against thermal recyclings counts against the possibility of nonrobust (trivial) or nonreproducible surface states. We further performed similar measurements of lowlying states focusing near the point (projection of the X_{3}) as shown in Fig. 2d. Similar spectra reveal ingap state features prominently around E_{B}~3–4 meV at T6 K, which clearly lie within the Kondo gap and exhibit similar (coupled) temperature evolution as seen in the spectra obtained near the point. This feature also disappears before reaching the Kondo hybridization scale, which is nonsuggestive of the possibility that this is the bottom of the conduction band. The fact that our sample is bulk insulating suggests that the Fermi level is not at the bottom of the conduction band, which would make the sample hugely metallic in transport. However, the surface Fermi level might also lie within the conduction band while it is bulk insulating which is another form of metallicity discussed in ref. 27.
On experimentally establishing the existence of ingap states, we study their momentumresolved structure or the kspace map for investigations regarding their topology: (1) the number of surface state pockets that lie within the Kondo gap; (2) the momentum space locations of the pockets (whether enclosing or winding the Kramers’ points or not). Figure 3a shows a Fermi surface map measured by setting the energy window to cover E_{F}±4 meV, which ensures the inclusion of the ingap states (that show temperature dependence consistent with coupling to the Kondo hybridization) within the Fermi surface mapping data as identified in Fig. 2c,d, at a temperature of 6 K inside the 2D transport anomaly regime under the ‘better than 5 meV and 7 K combined resolution condition’. Our Fermi surface mapping reveals multiple pockets that consist of an ovalshaped as well as nearly circularshaped pockets around the and points, respectively. No pocket was seen around the point, which was measured in a synchrotron ARPES setting. Therefore, the laser ARPES data capture all the pockets that exist while the bulk is insulating. This result is striking by itself from the point of view that while we know from transport that the bulk is insulating, ARPES shows large Fermi surface pockets (metallicity of the surface) at this temperature. Another unusual aspect is that not all Kramers’ points are enclosed by the ingap states. It is known that all trivial surface states must always come with even number of pockets, which include surface states that are due to reconstruction or surface polarity driven or surface impurity driven, since there is no way to get around the fermion doubling problem^{6}. Trivial surface states in nonmagnetic crystals must always come in pairs, otherwise a cornerstone of quantum mechanics, Kramers’ theorem would be violated^{6}. Another rigorous fact also mandated by the quantum mechanics on a lattice on general grounds is that for an inversion symmetric crystal (which is the case for SmB_{6}) harbouring spinorbit coupling large enough to invert the bulk bands (as in SmB_{6} according to all bulk band calculations), if Kramers’ theorem holds, the surface states cannot be degenerate at nonhighsymmetry points even if they are trivial (see, refs 4, 5, 6, 9). These conditions hold true irrespective of the chemical details or surface reconstruction or polaritydriven or danglingbond origin nature of the surface states, and allow us to count the Fermi surface pockets based on their momentum space winding in a Mod 2 count^{4,5,6,9}. Our observed Fermi surface thus consists of three (or odd number Mod 2 around each Kramers’ point) pockets per Brilluoin zone and each of them wind around a Kramers’ point only and this number is odd (at least three within our resolution). Therefore, our measured in(Kondo)gap states lead to a very specific form of the Fermi surface topology (Fig. 3) that is remarkably consistent with the theoretically predicted topological surface state Fermi surface expected in the TKI groundstate phase despite the broad nature of the contours. We further present the measured energymomentum cuts at 6 K (Fig. 3c,d) where lowenergy states consistent with the observed surface Fermi surface topology and their odd numbered crossing behaviour (Fig. 3a) are better identified than the kspace maps themselves (see Supplementary Discussion and Supplementary Figs S1–S5). The broadness is due to extremely small Fermi velocity especially near the zone centre. The Fermi velocity of the lowlying states is estimated to be less than 0.3 eV·Å and is consistent with the data; however, the details of dispersion within the Kondo gap are not well resolved, which is because of the finite quasiparticle lifetime broadening inevitable in a small Kondo gap material. This intrinsic lifetime, an expected effect, is elaborated and quantified with a numerical simulation in the Supplementary Discussion and Supplementary Fig. S2. Such broadening cannot be eliminated (not a resolution or data quality issue) as long as Kondo gap is on the order of 15–20 meV in a correlated material where sample mobility is on the order of several thousands cm^{2} V^{−1} sec^{−1}, which is the best possible scenario to this date.
Synchrotronbased ARPES measurements
Since for the laser ARPES, the photon energy is fixed (7 eV) and the momentum window is rather limited (the momentum range is proportional to , where hv is the photon energy and W4.5 eV is the work function), we utilize synchrotronbased ARPES measurements to study the lowlying state as a function of photon energy as demonstrated in Bibased topological insulators^{4,5,9}. Figure 4a,b shows the energymomentum cuts measured with varying photon energies. Clear E−k dispersions are observed (black dotted lines in Fig. 4b as a guide to the eye) within a narrow energy window near the Fermi level. The dispersion is found to be unchanged on varying photon energy, supporting their quasi2D nature (see, Fig. 4c). The observed quasi2D character of the signal within 10 meV where surface states reside does suggest consistency with the surface nature of the ingap states. Because of the combined effects of energy resolution (ΔE≥10 meV, although the sample temperature, 7 K, is near the anomalous transport regime) and the intrinsic selfenergy broadening coupled with the higher weight of the f part of the crosssection and the strong band tails (see Supplementary Discussion), the ingap states are intermixed with the higherenergy bulk bands’ tails. We speculate that the lack of k_{z} dispersion in the bands lying above 10 meV is due to some bandbending effect of the bulk bands that must occur in an intrinsic bulk insulator/semiconductor. A bentbulk band near a surface should naturally exhibit weak k_{z} dispersion since the effect is confined near the surface only. To isolate the ingap states from the bulk band tails that have higher crosssection at synchrotron photon energies, it is necessary to have energy resolution (not just the low working temperature) better than half the Kondo gap scale, which is about 7 meV or smaller in SmB_{6}.
Discussion
We now discuss the robust observations in our data and their connection to the theoretical prediction of the TKI phase. We have systematically studied the surface electronic structure of SmB_{6} at the transport anomaly regime (T6 K) where the transport character of the conduction electrons are predominantly 2D. We observe lowlying features extending to the Fermi level that lie inside the Kondo insulating gap. As the temperature is raised across the transport anomaly (beyond 7–8 K) and the Kondo lattice hybridization onset is approached, the ingap states (main features) become suppressed before reaching 30 K, which suggests that the dominant ingap states are contingent on the existence of strong and saturating Kondo hybridization and the existence of a robust and saturated insulating bulk gap. The ingap states are found to be robust and reproducible against thermal cycling of the sample in and out of the Kondo regime only, excluding the possibility of unrelated trivial surface states owing to dangling bonds or polaritydriven states that can robustly appear at much high temperatures owing to surface chemistry. Polaritydriven (nontopological) surface states must also come in even number of pockets at any high symmetry point of the BZ unrelated to the Kramers’ point topology. Furthermore, our kspace mapping covering the ingap states shows distinct pockets that enclose three (not four) Kramers’ points of the surface BZ, which are remarkably consistent with the theoretically predicted topological surface Fermi surface in the TKI ground state phase. Previous (and present) bulk band calculations have reconfirmed the strong role of spinorbit coupling in the bulk bands in this inversion symmetric material, which is suggestive of the surface states (trivial or nontrivial) on this compound being nondegenerate. This allows us to compare the surface states with theory that wind around the Kramers’ points. In the presence of bulk spinorbit coupling and band inversion, these surface states must carry 3π Berry’s phase, which is equivalent to π (3π Mod 2π). According to ref. 6, the most important criterion for a topological insulator is that of possessing odd number (1, 3, 5,...) of surface Fermi pockets of nondegenerate bands in a strong spinorbit system with bulk band inversion and the rest follows. These theoretical criteria directly imply a net surface Berry’s phase of π (ref. 6). Another independent way of proving a total 3π Berry’s phase in this system would be to carry out a direct spinARPES measurement as demonstrated previously in Bibased compounds in our earlier works (see reviews in refs 4, 5, 27). It is evident that the spinresolved measurements in this system is currently not feasible to address the same issue. The energy resolution of a spinARPES at synchrotrons is about 30–50 meV >>5 meV ingap state scale (see refs 28, 27)), and with laser, 14 meV >>5 meV (see ref. 29) and simultaneously accessible lowest temperature in combination with best spinresolution is about 20 K >>7 K, which is much larger than the 2D transport anomaly scale only within which surface states are unmixed with the bulk bands. Above 8 K, transport is 3D; therefore, bulk band must intermix in low energies. Since the Kondo gap is small, the intrinsic lifetime is large (see Supplementary Discussion) placing the system out of parameter range for all stateoftheart spinARPES measurement conditions. The fact that the surface states disperse in such a narrow Kondo gap of 10–15 meV that makes it difficult to track them with spinARPES also suggests that these states are quite interesting from the view point of interaction effects, and there does exist correlation effects in these surface states. This provides an exciting opportunity to study the interplay between Z_{2} order and electron–electron correlation via interface effects in future experiments. One exciting future direction to pursue would be to grow this material epitaxially on a suitable superconductor, which then via the proximity effect would enable superconductivity in a strongly correlated setting. Such superconductivity is likely to be unconventional. Regardless of the future works, our observed odd Fermi surfaces of the ingap states, their temperature dependence across the transport anomaly, as well as their robustness against thermal recycling, taken together collectively not only provide a unique insight illuminating on the nature of this 50yearold puzzle in heavy fermion physics but also serve as a future guideline to investigate other novel heavy fermion materials in connection to their exotic physics and transport anomalies.
Concurrently published articles (refs 30, 31) also report ARPES studies of SmB_{6} under various resolution and temperature conditions; however, many of the experimental details and interpretations of the data differ (in cases quite significantly) from ours.
Methods
Electronic structure measurements
Synchrotronbased ARPES measurements of the electronic structure were performed at the Synchrotron Radiation Center, Wisconsin, Advanced Light Source, Berkeley, and Stanford Radiation Lightsource, Stanford equipped with high efficiency R4000 electron analysers. Separate, highresolution and lowtemperature, lowphoton energy ARPES measurements were performed using a Scienta R4000 hemispherical analyser with an ultraviolet laser (hv=6.994 eV) at the Institute for Solid State Physics (ISSP) at the University of Tokyo. The energy resolution was set to be better than 4 and 10–20 meV for the measurements with the laser source and the synchrotron beamlines, respectively. The angular resolution was set to be better than 0.1° for the laser measurements and better than 0.2° for all synchrotron measurements.
Additional information
How to cite this article: Neupane, M. et al. Surface electronic structure of the topological Kondoinsulator candidate correlated electron system SmB_{6}. Nat. Commun. 4:2991 doi: 10.1038/ncomms3991 (2013).
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Acknowledgements
We thank P. W. Anderson, G. Bian, V. Galitski and D. Haldane for discussion. The work at Princeton and Princetonled synchrotron Xraybased measurements and the related theory at Northeastern University are supported by the Office of Basic Energy Sciences, US Department of Energy (Grants DEFG0205ER46200, AC0376SF00098 and DEFG0207ER46352). S.S. at ISSP acknowledges support from KAKENHI Grants number 23740256 and 2474021. T.D. at LANL acknowledges support from the Department of Energy, Office of Basic Energy Sciences, Division of Material Sciences and LANL LDRD program. We also thank M. Hashimoto, S.K. Mo and A. Fedorov for beamline assistance at the DOE supported Stanford Synchrotron Radiation Lightsource and the Advanced Light Source in Berkeley. M.Z.H. acknowledges Visiting Scientist support from LBNL, Princeton University and the A.P. Sloan Foundation. T.R.C. and H.T.J. are supported by the National Science Council, Taiwan. L.B. is supported by DOEBEZ through award DESC0002613.
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M.N., N.A., S.Y.X., T.K. and Y.I. performed the experiments with assistance from C.L., I.B., T.D., S.S. and M.Z.H.; D.J.K. and Z.F. provided samples that were characterized by Y.J.J., T.D., L.B. and Z.F.; T.R.C., H.T.J., H.L. and A.B. carried out band calculations; M.Z.H. was responsible for the conception and the overall direction, planning and integration among different research units.
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Supplementary Figures S1S6, Supplementary Discussion, Supplementary Methods and Supplementary References (PDF 655 kb)
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Neupane, M., Alidoust, N., Xu, S. et al. Surface electronic structure of the topological Kondoinsulator candidate correlated electron system SmB_{6}. Nat Commun 4, 2991 (2013). https://doi.org/10.1038/ncomms3991
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