Introduction

Topological insulator (TI) is a new class of matter with topologically protected surface states that possess unique electronic and spin properties1,2,3,4. Recently, how the topological order interplays with the electronic correlation has attracted a lot of theoretical considerations. As materials with significant correlations, the rare-earth borides are interesting with a variety of correlated phenomena including mixed valence, heavy fermion and superconductivity5,6,7,8,9,10,11. Especially, samarium hexaboride (SmB6) has recently been predicted to be a topological Kondo insulator12,13, which fueled intense effort in search for topological orders in correlated systems. Numerous experiments have been performed to identify surface states in SmB6 (ref. 14,15,16,17,18). Previous angle-resolved photoemission spectroscopy (ARPES) data shows that the bulk states coexist with the surface states with temperature down to 1 K and the insulating gap of SmB6 has found to be around 18 meV (ref. 15). Thus, it is important to search for materials with larger insulating gap or cleaner surface states in analogous to the topological SmB6.

YbB6 is a related rare-earth hexaborides which shares the same CsCl type crystal structure with SmB6 (ref. 19) and is predicted to be a moderately correlated TI with a bulk insulating gap of about 31 meV (ref. 20). With a larger band gap than that of SmB6, YbB6 might be another promising candidate for applications based on topological surface states. However, despite the previous successes of density functional theory in predicting TIs (ref. 2, 21 and 22), the correlations in rare-earth compounds pose challenges to an accurate calculation. For instance, the resistivity of YbB6 exhibits a bulk metallic behavior23, inconsistent with the prediction. Therefore, it is crucial to experimentally determine the electronic structure and topological nature of YbB6. ARPES is a powerful tool to directly measure the surface and bulk band dispersions and determine the value of topological invariant of three-dimensional TIs (ref. 3, 4 and 16). Furthermore, circular dichroism (CD) of the ARPES data have been shown to be related to the spin textures of the surface states15,24,25,26,27,28,29.

In this study, we report our ARPES measurements on YbB6 single crystals. Linearly dispersive bands were observed in its insulating gap around and with negligible kz dependences, indicative of their surface origins. The CD of these in-gap states at various photon energies show patterns consistent with the locked spin-momentum texture of TIs. The CD pattern of the α band around shows obvious two-fold symmetry, while the β band around presents anti-symmetric pattern about the axis in the surface Brillouin zone (BZ). Moreover, we found that the chemical potential varies up to about 500 meV, from one cleaved surface to another, or sometimes even across the same surface. The bulk bands often coexist with the topological surface states, however, we also identified a bulk insulating gap of about 100 meV, much larger than predicted20. It is thus possible to tune the chemical potential into such a gap and realize the surface states dominated transport.

Results

Sample characterizations

Sample preparation and experimental details are described in the Methods section. YbB6 crystallizes in the cubic Pm-3m space group and can be considered as the CsCl-type structure with the Yb ions and the B6 octahedra being located at the corner and the body center of the cubic lattice, respectively, as shown in Fig. 1(a). Figure 1(b) shows the bulk BZ together with the projected surface BZ. The high symmetry points we used are indicated in this panel. The X-ray diffraction pattern presented in Fig. 1(c) indicates a high sample quality of our single crystal and the natural surface is the (001) surface. The resistivity of YbB6 single crystal shows a metallic behavior down to 2 K (Fig. 1(d)), consistent with previous report in ref. 23, which can be further understood by the coexistence of the bulk band with the surface states that will be discussed below.

Figure 1
figure 1

Crystal structure and Sample characterization.

(a) Crystal structure of YbB6. (b) Bulk and surface Brillouin zone of YbB6 and the high symmetry points. (c) X-ray diffraction pattern of YbB6 single crystals. (d) Resistivity of YbB6 single crystals measured from 2 K to 300 K.

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Bulk valence bands and the linear-dispersive states

Figure 2(a) shows the photoemission intensity of YbB6 on sample 1 (S1) over a large energy scale, the non-dispersive Yb 4f bands are located at around 1 eV and 2.3 eV below Fermi energy (EF). They correspond to the 2F7/2 and 2F5/2 multiplets of the Yb2+ 4f14→4f13 final states based on the LDA calculation20. The energy difference between the two multiplets is 1.3 eV, consistent with the calculation. However, the energy positions of these 4f bands are deeper than that calculated in Ref. 20, suggesting correlation effects need to be reconsidered in calculation. In addition, some dispersive features are resolved in the low energy range, which may mostly originate from the Yb 5d orbitals20.

Figure 2
figure 2

Valence band structure and low-energy dispersive states of YbB6.

(a) Photoemission intensity plot showing the valence band structure of YbB6. The flat 4f bands are marked by the arrows. Data were taken along cut 1 of S1 at 6 K with 33 eV photons in SSRL. (b) Left: photoemission intensity map at EF taken with 31 eV photons at 6 K in SSRL. The intensity was integrated over a window of [EF - 10 meV, EF + 10 meV]. Right: the momentum cuts along which data were taken are marked in the projected two-dimensional BZ. (c) Top: the photoemission intensity plot along cut 2 taken on S2 with 91 eV photons at 18 K in SLS. Bottom: the same data after subtracting a momentum-independent background. The spectra far away from the dispersive region show no momentum dependence and thus taken as the background. The white lines indicate the α and γ bands, the dashed line is extrapolated from the linear dispersion. The red dashed line indicates the overlap of the band bottom of α and band top of γ. (d) The corresponding MDCs along cut 2 within [EF - 400 meV, EF - 150 meV]. The red line is the dispersion tracked from the MDC peaks and the red dashed line is extrapolated from the linear dispersion. (e) The photoemission intensity plot on S2 along cut 3 and cut 4 measured with 70 eV photons at 18 K in SLS. (f, g) The corresponding MDCs along cut 3 and cut 4 in panel (e), respectively. The red dashed lines are the dispersions of the β bands. The highlighted MDC in red indicates the possible energy position of the Dirac points. (h, i) The photoemission intensity plot on S3 along cut 5 and its corresponding energy distribution curves (EDCs) taken with 47 eV photons at 20 K in KEK, showing an additional δ band. (j) A schematic of all the bands observed along direction.

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The photoemission intensity map at EF on S1 is shown in Fig. 2(b). An elliptical Fermi pocket located around and a circular Fermi pocket around are clearly observed. The photoemission intensity distribution across taken on sample 2 (S2) is plotted in Fig. 2(c), together with a background subtracted one to visualize the dispersions more clearly. There is an electron-like band (referred to as α), forming the circular Fermi pocket in Fig. 2(b). In Fig. 2(e), another electron-like band is observed around (referred to as β), forming the elliptical Fermi pocket.

Both the α and β bands exhibit almost linear dispersions as can be seen from their momentum distribution curves (MDCs) in Figs. 2(d), 2(f) and 2(g). The α band extrapolates to cross at about 380 meV below EF. There is also a γ band below the α band. However, the band bottom of α overlaps with the band top of γ in certain energy range as highlighted in Fig. 2(c). This observation, together with the very different intensities of γ and α, indicates that γ is not the lower cone of α, if there is a Dirac point as predicted20. Due to the low intensity of the α band and the interference of the strong γ band, the lower cone is hardly resolved, if any.

The β band also seems to cross at about 320 meV below EF by tracking its linear dispersion, but the predicted lower cone could not be distinguished either, due to the strong residual intensity of the flat 4f bands. The δ band is only observed within a narrow photon energy range [e.g. 47 eV in Fig. 2(h)] with its band bottom around −80 meV measured on sample 3 (S3). The band bottom of β in S3 is around −250 meV, different from that in S2, which may be caused by the difference in their chemical potentials. Figure 2(j) is the schematic of all the low-lying energy bands resolved along direction.

Photon energy dependence of the linear-dispersive bands

Photon energy dependent ARPES experiments have been performed to examine how the α, β and γ bands vary with kz. The photoemission intensity distributions taken with different photon energies are presented in Fig. 3. One can see that, for both α and β bands, although the spectral weight varies with photon energy due to photoemission matrix element effects, the dispersions of them remain unchanged. Figures 3(a) and 3(b) show the photoemission intensity distributions across on sample 4 (S4) together with their corresponding MDCs. We fitted the dispersion of the α band taken with 94 eV photons and overlaid it onto the data taken with several other photon energies, which clearly show that the dispersion of α is kz independent. The same process has been done to the β band in Figs. 3(c) and 3(d), which also show no kz dependence. More data under other photon energies can be found in the Supplementary Information (SI).

Figure 3
figure 3

Photon energy dependence of the α, β and γ bands.

(a, b) Photon energy dependence of the photoemission intensity of the α band measured along cut 2 on S4 and its corresponding MDC plots within [EF -200 meV, EF]. (c, d) The same for the β band as in panel (a) and (b) measured along cut 3 on S4. (e, f) Photon energy dependence of the photoemission intensity of the γ band measured along cut 2 on S2 and its corresponding MDC plots within [EF -600 meV, EF -360 meV]. The data in panel (e) is subtracted by a momentum-independent background. The spectra far away from the dispersive region show no momentum dependence and thus they are taken as the background. The red dashed lines in panel (b), (d) and (f) are fitted dispersions with 94 eV data of the α and β bands and with 103 eV data of the γ band, respectively and overlaid them onto the data of other photon energies. The white dashed lines in panel (e) are extracted from the 103 eV data indicating the α and γ bands and overlaid them on top of data with other photon energies. (g–j) Photoemission intensity plots in the kz-kx plane at EF, EF-150 meV, EF-450 meV, EF-600 meV, respectively. The intensity was integrated over a window of [EF - 10 meV, EF + 10 meV]. The red dashed lines indicate the dispersions of the α, β and γ bands along kz direction. Data were taken at 18 K in SLS.

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However, in Figs. 3(e) and 3(f), when we overlaid the dispersion of γ extracted from the MDCs taken with 103 eV photons on top of the data taken with several other photon energies, there are clear mismatches. That is, the γ band disperses with kz, indicative of its bulk origin. Furthermore, the dark interior of intensity envelopes of the γ band in Fig. 3(e) is likely due to its dispersion along kz and the poor kz resolution in ARPES measurements with vacuum ultraviolet photons. Similar behavior has been reported for a bulk band in SmB6 (ref. 15). The band top of the valence band (γ band) observed here is located at the point, which is quite different from the theoretical calculation where the top of the valence band is around the point20. We also note that our observation of the γ band is consistent with another ARPES data reported recently30. Such a sharp contradiction between the experiment and theoretical calculation calls for further understanding of YbB6.

Moreover, the kz-kx intensity plots at EF, EF-150 meV, EF-450 meV, EF-600 meV are shown in Figs. 3(g)–3(j) assuming the chemical potential to be 15 eV, which clearly show the evolution with kz of these bands. The crossings of the α band and the β band remain unchanged (Figs. 3(g) and 3(h)), consistent with the two-dimensional nature of them. However, the data at EF-450 meV and EF-600 meV in Figs. 3(i) and 3(j) clearly show the variation of the γ band with different kz’s. The evident dispersion along kz further indicates its bulk origin. This assignment is consistent with a recent bulk sensitive soft X-ray ARPES study on YbB6 (ref. 30).

The δ band is only observed in certain photon energies, due to different cross-section of this band. The lineshape of the δ band is hardly resolved due to its bulk origin and poor kz resolution, which results in a bright interior of intensity envelopes of the δ band. Thus the δ band should be the bulk conduction band, which can well explain the metallic resistivity behavior in YbB6 (see Fig. 1(d)). As the band bottom of the δ band in S3 is around −80 meV, the band bottom of δ in S2 should be around −150 meV, due to the 70 meV difference in chemical potential between these two samples (see SI). Moreover, since the band top of γ in the 91 eV data of S2 locates at around −250 meV [Fig. 2(c)], the bulk band gap of YbB6 is likely to be about 100 meV, as illustrated in Fig. 2(j). This determined gap size is much larger than the theoretical prediction of only 31 meV (ref. 20), which suggests the correlation effects need to be better treated in the calculations.

The circular dichroism of the linear-dispersive bands

The chirality of spin and orbital angular momentum (OAM) is another remarkable hallmark of the topological surface state, since both of them are interlocked and rotate with the electron momentum, so that the total angular momentum is conserved. To further explore the topological nature of these surface states, we conducted CD-ARPES experiment, which probes the chirality of the OAM15,28.

The Fermi surface maps of S1 measured under right-handed circular polarized (RCP) light and left-handed circular polarized (LCP) light are shown in Fig. 4(a), together with their difference (referred to as RCP-LCP). The CD of the β pocket shows an anti-symmetric pattern about the axis in the surface BZ. The enlarged CD image near is shown in Fig. 4(b). Although its intensity is much weaker than that of the β pocket, we can see that the symmetry of the α pocket becomes two-fold, which is different from the anti-symmetric CD pattern of the β pocket. Such symmetries are confirmed by another set of data with more statistics in the top panel of Fig. 4(c), which was measured on S4 with 35 eV photons, showing the α pocket and the right β pocket. The bottom panel in Fig. 4c is measured on sample 5 (S5), under the same condition as S2, but presents the left β pocket. Clearly, all the CD patterns exhibit an inversion symmetry with respect to .

Figure 4
figure 4

Circular Dichroism of the surface states around and .

(a) Fermi surface maps of YbB6 taken with RCP, LCP light and their difference (RCP-LCP) of S1. The intensity was integrated over a window of [EF - 10 meV, EF + 10 meV]. (b) The RCP-LCP data around enlarged from panel (a). (c) Top: CD result of S4 (top) and S5 (bottom) measured with 35 eV photons showing the right pocket and the left pocket, respectively. (d) The CD values taken along the left pocket around in panel (a) of S1 as a function of the polar angle Ω. Ω is defined within panel (a) respect to . (e) The same as that in panel (d) to show the CD of α pocket taken on S4, where Ω is defined within panel (c) respect to . The red solid curves in panel (d) and (e) are sine function fits of the data. The 31 eV data were taken at 6 K in SSRL and the 35 eV data were taken at 18 K in SLS.

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Moreover, we observe a sign change between the 31 eV and 35 eV CD data in both the α and β pockets. This simultaneous sign change can be attributed to a final-state effect of the CD-ARPES as reported in Bi2Se3 (ref. 24). In Figs. 4(d) and 4(e), we plot the representative CD distributions around the α and β pockets. Both of them can be well fitted by a sine function, however, the period for β is 2π, while that for α is π. The reductive period of the α band, or the two-fold symmetric CD pattern needs further investigation, but similar behaviors were attributed to the coupling to bulk states in Bi2Se3 and Bi2Te3 (ref. 29, 31,32,33). Despite the intriguing symmetry, the CD results do suggest that the chirality of OAM exist in both the α and β bands, indicating that they might possess helical spin textures.

From the data above, the surface nature and the possible topological origin of the α and β bands have been established. We also note that there is one Fermi pocket around and two Fermi pockets around in the surface BZ, the total number of surface states is odd, thus the whole system should be topologically non-trivial. This is remarkably consistent with the theoretical prediction that YbB6 is a Z2 TI (ref. 20).

The variation of surface chemical potential

We found that the chemical potential varies during different samples. In most cases the variation is within 100 meV and the band structure is similar as discussed above. But sometimes, we observed very different, hole-like pocket around , referred to as β' in Figs. 5(a) –5(c). The electron-like Fermi pocket and the hole-like Fermi pocket can be even observed in different regions of the same sample, which may be due to inhomogeneous doping of the sample or different surface conditions. The chemical potential of the sample with hole-like pockets (S6) differs 490 meV from that of S2 with electron-like pockets, indicated by the shift of the 4f bands between these two samples shown in Fig. 5(d). Since the linear extrapolation of β' in S6 leads to a crossing at around 180 meV above EF and the crossing point of β is located at around 320 meV below EF, the energy position of the crossing point shifted about 500 meV. This is consistent with the 490 meV shift of the 4f bands within error bar, indicating that β' could be the lower half of the possible Dirac cone of β. The slope of β near its crossing point and the slope of β' are nearly same with only 4% difference, further support they are from one Dirac cone. Around , on the other hand, we did not resolve the band below the crossing of α, which could be concealed by the bulk band γ.

Figure 5
figure 5

Hole-like surface in YbB6 and temperature dependent electronic structure of electron-like surface in YbB6.

(a) Left: Photoemission intensity map of S6 with hole-like pockets. The intensity was integrated over a window of [EF - 10 meV, EF + 10 meV]. Right: the momentum cuts along which the data were taken are marked in the projected two-dimensional BZ. (b, c) Two photoemission intensity plots taken along cut 6 and cut 7 indicated in panel (a) by the blue arrows, respectively. The hole-like dispersions are indicated by the dashed lines. Data were taken on S6 at 20 K with 47 eV photons in KEK. (d) A schematic plot to show the chemical potential shift in different surfaces and the integrated EDCs of the two different surface to compare the different chemical potential. μ2 and μ6 refer to the chemical potential of the two different cleaved surfaces of S2 and S6. (e) The photoemission intensity data taken along direction at 6 K and 196 K, respectively. Data were taken on S1 at SSRL with 31 eV photons.

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Temperature dependence of the electronic structure

The observed surface states in YbB6 are robust against the change of temperature from 6 K to 196 K [Fig. 5(e)]. This is consistent with the theoretical calculations which show that YbB6 is a moderately correlated insulator but not a Kondo insulator20.

Conclusion

To summarize, we have obtained a comprehensive understanding of the electronic structure of YbB6 from ARPES. We directly observed several linearly dispersive bands within the insulating gap of YbB6 that show negligible kz dependence. The CD-ARPES data indicate well-defined helical spin texture of the surface states. These results suggest that YbB6 is a TI. We note that the sensitivity of chemical potential reported here also implies its tunability. If the chemical potential can be tuned into the 100 meV insulating gap, the topological surface state can be exploited in applications without the interference from the bulk states.

Methods

Sample synthesis

High quality YbB6 single crystals were synthesized by the Al-flux method. A chunk of Yb together with the powders of Boron and Al were mixed with a ratio of 1:6:400 and heated to 1773 K in an alumina crucible in the argon atmosphere, then maintained at 1773 K for about 2 days before slowly cooling down to 873 K at a rate of 5 K per hour.

ARPES measurement

ARPES measurements were performed at the SIS beamline of Swiss Light Source (SLS) and Beamline 5-4 of Stanford Synchrotron Radiation Lightsource (SSRL), both equipped with a Scienta R4000 electron analyzer and beamline 28A of Photon Factory, KEK, equipped with a Scienta SES-2002 electron analyzer. The angular resolution was 0.3°and the overall energy resolution was better than 15 meV depending on the photon energy. The samples were cleaved in situ along the (001) plane and measured under ultra-high vacuum below 5×10−11 torr.