Different evolution of the intrinsic gap in strongly correlated SmB 6 in contrast to YbB 12

. Dependence of the spectral functions near the Fermi level on temperature and rare-earth atom doping was studied in detail for strongly correlated alloys Sm 1 − x Eu x at ∼ 8000 eV as well as at 7 and 8.4 eV. It was found that the 4f lattice coherence and intrinsic gap are robust for Sm 1 − x Eu x B 6 at least up to the Eu substitution of x = 0 . 15 while both collapse by Lu substitution already at x = 0 . 125 for Yb 1 − x Lu x B 12 . As for the temperature dependence of the spectral shapes near the Fermi level at low temperatures, rather contrasting results were observed between YbB 12 and SmB 6 . Although the gap shape does not change below 15 K for YbB 12 with the characteristic temperature T ∗ of 80 K, the spectral shape of SmB 6 with a T ∗ of 140 K shows that the peak beyond the gap is further increased below 15 K. The temperature dependence of the spectra near the intrinsic gap is clearly different between SmB 6 and YbB 12 , although both materials have so far been categorized in the same kind of strongly correlated semiconductor. The possibility of the surface contribution is discussed for SmB 6 .

at ∼8000 eV as well as at 7 and 8.4 eV. It was found that the 4f lattice coherence and intrinsic gap are robust for Sm 1−x Eu x B 6 at least up to the Eu substitution of x = 0.15 while both collapse by Lu substitution already at x = 0.125 for Yb 1−x Lu x B 12 . As for the temperature dependence of the spectral shapes near the Fermi level at low temperatures, rather contrasting results were observed between YbB 12 and SmB 6 . Although the gap shape does not change below 15 K for YbB 12 with the characteristic temperature T * of 80 K, the spectral shape of SmB 6 with a T * of 140 K shows that the peak beyond the gap is further increased below 15 K. The temperature dependence of the spectra near the intrinsic gap is clearly different between SmB 6 and YbB 12 , although both materials have so far been categorized in the same kind of strongly correlated semiconductor. The possibility of the surface contribution is discussed for SmB 6 .
states have been reported in SCES semiconductors (not only SmB 6 [6] 15 and YbB 12 [7] but also Ce 3 Bi 4 Pt 3 [8] and FeSi [9]). Various theoretical approaches have been proposed to interpret the evolution of the 'large' and 'small' gaps as well as the VF behavior by means of the Wigner lattice model [10], the exciton-polaron model [11] and the Anderson lattice model at halffilling [12]. Despite numerous experimental and theoretical studies, the origin of the gap states has not been fully clarified yet [13][14][15].
Photoelectron spectroscopy (PES) is a powerful tool to directly determine the spectral density of states (DOS) as well as quasiparticle band structures. To date, PES studies, usingconventionalphotonenergies(hν∼20-125eV),havebeenperformedforSmB 6 [4] (seefootnote13)andYbB 12 [16,17] 16 . These conventional PESs have, however, the inherent character of surface sensitivity due to the short inelastic mean-free path (IMFP) of photoelectrons (∼5 Å) [18]. Since the surface of such SCES semiconductors can be metallic [19], more bulk-sensitive PES studies are desired. Recently, hard x-ray PES (HAXPES) has widely been recognized as a highly bulk-sensitive technique because of the long IMFP and applicability to various SCES [20,21]. The IMFP reaches up to ∼100 Å at hν ∼ 8 keV [18]. Recently, extremely low-energy (hν < 10 eV) PES (ELEPES) with excitations by lasers, synchrotron radiation (SR), or Xe and Kr resonance lines has also become popular as a rather bulk-sensitive ultra-high-resolution technique [22][23][24][25][26]. The IMFP for ELEPES is expected to be comparable with that for HAXPES under certain conditions. Thus, combined HAXPES and ELEPES studies are thought to be extremely useful for revealing intrinsic bulk electronic structures of SCES.
In our HAXPES for the SCES alloys Yb 1−x Lu x B 12 [27] 17 , it is concluded that the Yb 4f lattice coherence, being effective for x = 0, collapses easily by Lu substitution (already at x = 0.125). In addition, optical studies have independently shown the gap collapse for x = 0.125 [28] 18 . It is thus deduced that the Yb 4f lattice coherence plays an essential role for the gap formation in pure YbB 12 . In the INS studies [29] 19 , however, it was suggested that the spin gap of ∼10 meV as well as a broad INS peak around ∼38 meV could be driven by the Yb 4f single-site effects because these were robust up to x = 0.9. A polarized neutron study was later performed on single-crystal YbB 12 between 5 and 125 K [30], where three peaks were observed at ∼14, ∼18 and ∼40 meV at the L point with the wave number q = (0.5, 0.5, 0.5). The results did not support, however, that the peak at ∼40 meV was due to the single-site effect from its q dependence. To fully understand the origin of the gaps in SCES semiconductors, the competition between 4f lattice coherence effects and 4f single-site effects must be carefully studied in various cases. Here, we report on bulk-sensitive HAXPES as well as ELEPES on Sm 1−x Eu x B 6 and Yb 1−x Lu x B 12 including their doping and temperature dependence and discuss the changes of their electronic structures. 15 The gap of ∼3 meV below 15 K was interpreted as being due to an excitation from an additional narrow donortype band located at ∼3 meV below the bottom of the upper conduction band. 16 Measurements at hν = 21.2 and 40.8 eV were performed on scraped surfaces of single crystals. 17 The peak at ∼36 meV in YbB 12 was interpreted as being due to the Kondo resonance peak. However, the temperature dependence of its peak energy is beyond the prediction by the single-impurity Anderson model. 18 For YbB 12 , the optical conductivity spectrum showed a clear energy gap with an onset at ∼20 meV and a shoulder at 38 meV. With the increase of x in Yb 1−x Lu x B 12 , the gap is rapidly collapsed leaving a shoulder at ∼40 meV. 19 Spin gap is defined as the energy threshold below which no magnetic signal can be detected in INS.

3.Resultsanddiscussion
Figure1(a)showsthedopingdependenceoftheHAXPESspectraat20and200Kfor Sm 1−x Eu x B 6 withx=0,0.15and0.5.Forcomparison,theresultsofYb 1−x Lu x B 12 withx=0 and0.125arealsoreproducedfrom [27](seefootnote17)infigure1(b).Athν∼8keVthe photoionization cross sections [34] of Sm and Yb 4f states are higher than those of B 2sp and RE 5d states. Therefore, the spectra near E F at hν ∼ 8 keV are dominated by the excitations f 6 → f 5 for Sm 2+ (4f 6 ) and f 14 → f 13 for Yb 2+ (4f 14 ) states 20 . The broad peaks for Sm 1−x Eu x B 6 consist of the Sm 4f 5 ( 6 H 5/2 and 6 H 7/2 ) final-state multiplets [35] (vertical line spectra in figure 1(a)), whereas the single peaks for Yb 1−x Lu x B 12 are ascribed to the Yb 4f 13 7/2 final state. In figure 1(a), the Sm 4f 5 peaks for x = 0 and 0.15 in Sm 1−x Eu x B 6 clearly show the energy shift toward E F on going from 200 to 20 K in contrast to the negligible shift for x = 0.5, when the spectra were fitted with Lorentzian (for the slight lifetime broadening) and Gaussian (for the instrumental resolution) broadened functions as shown by the solid lines. The relative intensity and energy for the Sm 4f multiplets were properly taken into account [35].
The estimated Sm 4f peak shift toward E F on cooling for x = 0 and 0.15 is ∼40 meV, while that for x = 0.5 is less than 10 meV in Sm 1−x Eu x B 6 . On the other hand, the Yb 4f peak shift toward E F is ∼20 meV for x = 0 whereas it is at most 10 meV for x = 0.125 in Yb 1−x Lu x B 12 (figure 1(b)). As argued previously for YbAl 3 [36,37] 21 but not for YbInCu 4 [38] 22 , peak shifts with temperature of this magnitude are greater than predicted in the single-impurity Anderson model and so are considered to be a 4f lattice coherence effect. The temperature dependence of the 4f peaks observed for x = 0 and 0.15 in Sm 1−x Eu x B 6 is qualitatively similar to that for pure YbB 12 and YbAl 3 in which the Yb 4f lattice coherence is essential for the peak shift. 20 The 4f 6 multiplets from the Eu 2+ (4f 7 ) state for Sm 1−x Eu x B 6 (x = 0.15 and 0.5) and the 4f 13 doublets from the Lu 3+ (4f 14 ) state for Yb 1−x Lu x B 12 (x = 0.125) are observed as the localized states in 1-2 and 7-9 eV, and they do not contribute directly to the spectral changes near E F . 21 Negligible thermal shift was observed for the 4f peak (4f 13 J = 7/2 final state) of Yb 0.6 Lu 0.4 Al 3 in contrast to that in YbAl 3 . 22 In this case, the 4f peak shift as a smooth function of temperature and the Yb 4f lattice coherence were not discussed because of the bulk valence transition at around 42 K. [27](seefootnote17).Thecirclesandsolidlines indicate the experimental data and the fitting results (see text). The spectra are normalized for different x by the integrated intensity in the binding energy range of −0.2 eV E B 0.6 eV for Sm 1−x Eu x B 6 and −0.2 eV E B 0.8 eV for Yb 1−x Lu x B 12 at each temperature.

Figure1.HAXPESspectraat20and200Kfor(a)Sm
In this sense, the Sm 4f lattice coherence survives not only for x = 0 but also for x = 0.15 in In order to study the relation between the gap formation and the 4f lattice coherence by overcoming the resolution limit of HAXPES, we have performed the ELEPES with much higher energy resolution. The doping-and temperature-dependent ELEPES spectra near E F for Sm 1−x Eu x B 6 and Yb 1−x Lu x B 12 are presented in figures 2(a) and (b). Here the observed spectra are dominated by the non-RE 4f states, i.e. B 2sp and RE 5d states [34] hybridized with the Sm or Yb 4f states in contrast to the case of HAXPES.
In SmB 6 , the spectral weight at E F decreases clearly and the peak narrows and shifts toward E F on decreasing the temperature from 200 to 5 K. The so-called leading edge of the spectra is clearly observed on the occupied state side below E F , demonstrating finite gap formation at low temperatures. The spectra show a prominent peak at ∼19 meV below 15 K. In the surfacesensitive HeI PES spectra on fractured surfaces [4], the background with E B above 40 meV is relatively higher than in the present ELEPES spectra and the increase in the peak intensity between 30 and 5.7 K is much smaller than that in ELEPES between 15 and 5 K.
The spectra of Sm 1−x Eu x B 6 with x = 0.15 measured at hν = 7 eV show rather similar temperature dependence to that of SmB 6 except for the peak energy positions while the spectra for x = 0.5 show a typical metallic thermal behavior even at low temperatures without a prominent peak and gap opening. The prominent peak for x = 0.15 Sm 1−x Eu x B 6 at low temperatures has also been observed at the same binding energy in several other spectra measured at hν between 7 and 12 eV (not shown here). The bulk origin of this peak is confirmed by the increase of its intensity on decreasing hν as 12 → 9.7 → 8.4 → 7 eV in accordance with the increase in the IMFP or bulk sensitivity. The relative increase of this peak intensity compared with the intensity above E B ∼ 50 meV after slight in situ surface degradation over 20 h under ∼7 ×10 −8 Pa at hν = 7 and 17 eV also supports the bulk origin of this prominent peak. In transport The inset of (b) describes the doping dependence of the spectra for Yb 1−x Lu x B 12 at 5 K. The intensity of all these spectra is normalized at E B = 100-120 meV, where the spectra show no temperature dependence in both systems.
measurements, an exponential increase in the electrical resistivity due to the gap formation on cooling has been observed for x 0.2 Sm 1−x Eu x B 6 [39] 23 , consistent with the present ELEPES results.
In the case of YbB 12 , the spectra show a slight but still noticeable decrease of the intensity at E F upon cooling, suggesting gap formation ( figure 2(b)), where two peaks are observed at 15 and 45 meV at low temperatures (indicated by arrows), being qualitatively similar to the previous work by SR at hν = 15.8 eV [40]. For the Lu doping up to x = 0.125, the two peaks are located at almost the same positions. However, a clear difference between x = 0 and 0.125 is seen at 5 K as shown in the inset of figure 2(b) as the intensity around E F is definitely higher for x = 0.125, suggesting a collapse of the 'small' energy gap.
A clear feature to be noted here is a different temperature dependence between SmB 6 and YbB 12 in the range of 5-15 K, which are far below the characteristic temperature T * . Namely, the spectral weight of the narrow peak is further enhanced from 15 to 5 K for SmB 6 (T * ∼ 140 K) while such a temperature dependence is absent for YbB 12 (T * ∼ 80 K) as more clearly seen later in figures 3(c) and (f). These contrasting results require some new scenario to interpret the results of SmB 6 since the electronic state of YbB 12 is almost in the ground state at 15 K (T * ∼ 80 K), whereas that of SmB 6 appears to be not in the ground state even at 15 K (T * ∼ 140 K). Sm 2p 3/2 (L 3 ) edge absorption spectra of SmB 6 were recently reported [41], where the Sm valence was found to slightly increase toward 3+ below 15 K on decreasing the temperature. Under this condition, the 4f occupation number may decrease and the 4f 5 PES final state intensity may also decrease. (As already mentioned, the observed peak in ELEPES is due to the B 2sp and Sm 5d state hybridized with the Sm 4f state. So the peak intensity near the Fermi level does not directly reflect the Sm 4f weight in contrast to HAXPES [42].)   [29](seefootnote19)andthoughtnotto correspond to the observed structures in the photoelectron spectra. The Kondo peak of YbB 12 was observed at ∼36 meV in HAXPES at low temperatures below 20 K as shown in figure 1(b). The observed structure in figure 3(d) at ∼45 meV is not directly representing the Kondo peak with dominant Yb 4f character because of the dramatically decreased relative photoionization cross section of the Yb 4f states at hν = 8.4 eV [34]. Although the origins of the observed structures in YbB 12 in photoelectron spectra at hν of 15.8 and 100 eV and INS in the similar energy region were compared and discussed [40,44], interpretation is still not settled 24 .
The gap of YbB 12 observed in the present ELEPES experiment is tentatively estimated to be ∼10 meV according to the definition as applied to SmB 6 (see the inset of figure 3(d)), consistent with the 'large' gap reported by the electrical resistivity [5]. As seen in figures 3(d) and 2(b), the intensity at E F for YbB 12 decreases upon cooling as indicated by the full (red) triangles in the inset of figure 3(e), where it starts to reduce steeply below 50 K. However, the intensity decrease at E F is much less for x = 0.125 Yb 1−x Lu x B 12 as shown by the empty (blue) triangles in the inset of figure 3(e). The direct comparison of DOS between x = 0 and 0.125 at low temperatures is shown in figure 3(f). It is found that the DOS minimum near E F recovers noticeably for x = 0.125 even at 5 K. This energy scale less than ∼7 meV is comparable with the magnitude of the 'small' gap [5]. We conclude that the small gap ( S 7 meV) collapses even at low temperatures with Lu substitution of x = 0.125, whereas the large gap ( L 10 meV) remains still. From the doping dependence of these two gaps for Yb 1−x Lu x B 12 , we conclude that 24 Two peaks were observed at ∼50 and ∼15 meV at low temperatures below ∼60 K at hν = 15.8 and 100 eV. The ∼15 meV peak was interpreted as due to hybridization between the Yb 4f and Yb 5d states in [40]. INS on singlecrystal YbB 12 showed spin gap structure with two sharp, dispersive, in-gap excitations at ∼14.5 and ∼20 meV. The former peak was ascribed to the short-range correlation near the antiferromagnetic wave vector [44]. the'small'gapcollapseswhenthe4flatticecoherenceisbroken,whilethe'large'gapsurvives inthisYb 1−x Lu x B 12 systembecauseitisinducedbythe4fsingle-siteeffects.Thespingap, robustlydetecteduptox=0.9intheINSforYb 1−x Lu x B 12 [29](seefootnote19),mighthave suchacharacterasthepresentlyobserved'large'gap.
In the case of the present ELEPES of SmB 6 , the opening of the bulk 'large' gap below 100 K is clear (inset of figure 3(b)). The explanation of the peak intensity increase in SmB 6 from 15 to 5 K is difficult as long as we consider only the valence increase of bulk electronic states [41]. Here one may think of a possible contribution of the surface. The ELEPES, which was often claimed and confirmed to be bulk sensitive, is, however, now known to show noticeable surface sensitivity depending upon the individual materials and experimental conditions, including the binding energies of the probed electronic states [26,48].
Recently, a theoretical prediction that some of the Kondo insulators (semiconductors) can have a metallic surface and can be classified into a three-dimensional topological insulator has been attracting wide attention [49,50]. Among them, SmB 6 was proposed to be a promising candidate for a strong topological insulator [51], where metallic surface states were claimed to correspond to the so far not fully explained in-gap states. If such a metallic state induced by the momentum-dependent hybridization between the crystal field split Sm 4f state and conduction electron states takes place on the surface due to the strong spin-orbit coupling on f sites, the surface electronic structures may still have freedom at low temperatures even below 15 K [50]. The increase of the peak intensity at ∼19 meV below 15 K may somehow be related to this surface state as also discussed in [46]. According to the band calculation in [51], metallic surface states with a Dirac cone are predicted near the surface point and surface X points which are characteristic for the topological insulator. Then spin polarization may be observed for such states. In addition, surface bands with the bottom at the surface X point are predicted [51] extending upward and crossing the Fermi level in the middle region between the surface and X points. The latter bands have a bottom at ∼14 meV, where the DOS may have a maximum. If the gap opens in the bulk electronic states, the relative spectral weight of the surface electronic states against the bulk electronic states may increase. For example, the surface state was very clearly observed on the Cu(111) surface by angle-resolved ELEPES at hν ∼ 8.4, 10.0 and 11.6 eV [26]. The angle-resolved ELEPES could also resolve the Dirac cone of the surface metallic state of a topological insulator Bi 2 Te 3 [48]. Thus, the ELEPES on SmB 6 might have enabled us to partially probe the DOS of surface states also under the present ELEPES condition. If metallic states are present on the topological insulator surface after the intrinsic gap opening, the surface state may become sensitively observable in the gap energy region below E F . So one of the plausible interpretations of the present ELEPES results of SmB 6 at low temperature (15-5 K) is to consider the contribution of this surface state DOS overlapping with the prominent bulk peak in the region of ∼19 meV. In this scenario, the sharp bulk peak at ∼19 meV associated with the 'large' gap opening will show an intensity increase between 15 and 5 K due to the increase of the background overlapping in this energy region resulting from the surface bands, which become observable with slightly higher intensity by the opening of the gap. For further discussions, spin-and angle-resolved photoelectron spectroscopy with different bulk or surface sensitivity is necessary. Point-contact spectroscopy [52] as well as scanning tunneling spectroscopy may also be useful for the study of these electronic structures.

Conclusions
In conclusion, a combination of ELEPES and bulk-sensitive HAXPES is found to be a very powerful method for studying electronic structures of SCES semiconductors. It is found that the 4f lattice periodicity is essential for the gap formation and collapse in Yb 1−x Lu x B 12 in a certain x range below x = 0.125 and in Sm 1−x Eu x B 6 in a certain x range below x = 0.5 at low temperatures. Although the electronic ground state is achieved at 15 K in YbB 12 with T * ∼ 80 K, the electronic states are still not in the ground state at 15 K in SmB 6 with T * ∼ 140 K. Even the bulk valence change below 15 K cannot explain the increase of the intensity of the peak at ∼19 meV in SmB 6 below 15 K. The observed unusual behavior of ELEPES spectral shapes in SmB 6 is thought to be possibly due to the overlap of some surface contribution. Further spinand angle-resolved high-resolution photoelectron spectroscopy will ascertain the validity of this possible scenario in the near future.