Surface Kondo effect and non-trivial metallic state of the Kondo insulator YbB12

A synergistic effect between strong electron correlation and spin–orbit interaction has been theoretically predicted to realize new topological states of quantum matter on Kondo insulators (KIs), so-called topological Kondo insulators (TKIs). One TKI candidate has been experimentally observed on the KI SmB6(001), and the origin of the surface states (SS) and the topological order of SmB6 has been actively discussed. Here, we show a metallic SS on the clean surface of another TKI candidate YbB12(001) using angle-resolved photoelectron spectroscopy. The SS shows temperature-dependent reconstruction corresponding to the Kondo effect observed for bulk states. Despite the low-temperature insulating bulk, the reconstructed SS with c–f hybridization is metallic, forming a closed Fermi contour surrounding on the surface Brillouin zone and agreeing with the theoretically expected behaviour for SS on TKIs. These results demonstrate the temperature-dependent holistic reconstruction of two-dimensional states localized on KIs surface driven by the Kondo effect.

R ecently, non-trivial surface electronic structures such as surface metallic states of topological insulators 1,2 and giant Rashba-type spin splitting of polar semiconductors [3][4][5] have been observed. These electronic structures originate from the large spin-orbit interaction (SOI) of heavy elements. On the other hand, in metallic compounds containing heavy elements, especially rare-earths, heavy quasiparticles, namely heavy fermions, appear owing to the Kondo effect 6 . The origin of the Kondo effect is a hybridization between the conduction band and localized states (for example, 4f states of rare-earths), namely, c-f hybridization, derived from the Anderson model. At the surface of rare-earth intermetallic compounds, new physical properties originating from the Kondo effect and the large SOI such as superconductivity without inversion symmetry 7 will appear. Kondo insulators (KIs) are one candidate of such compounds.
In general, KIs possess a small energy gap (typically a few tens of meV) at the Fermi level (E F ) owing to c-f hybridization at low temperatures 8 . In the case that the c-f gap is formed by the conduction and valence bands with inverted parities, two-dimensional (2D) metallic electronic states should always appear on the KI surface as in the case of topological insulators 9,10 . Such materials are categorized as topological Kondo insulators (TKIs) in which the topological surface states (SS) originate from c-f gap formation owing to the Kondo effect. Thus, TKIs are new physical states of quantum matter driven by the synergistic effect between strong electron correlation and SOI.
The surface state of the KI samarium hexaboride (SmB 6 ) has been investigated both theoretically and experimentally [11][12][13][14][15][16] and has been theoretically predicted to be a non-trivial topological surface state of a TKI. This predicted surface electronic structure has been experimentally observed [12][13][14][15] . However, the origin of the metallic surface state is currently under debate because Hlawenka et al. recently reported that the surface metallic state trivially originates from large Rashba splitting 16 . Therefore, a survey of another material is desirable to provide further insight into the origin of metallic SS on KIs.
Ytterbium dodecaboride (YbB 12 ) is a typical KI which has a NaCl-type crystal structure with Yb and B 12 clusters 17 . A clear energy gap appears in the bulk of YbB 12 with a gap size of about 40 meV of the peak (15 meV of the onset), which has been observed by an optical conductivity measurement 18 . Using angleintegrated photoemission measurements, a pseudo-gap opens at E F , but a finite density of states has been observed at temperatures lower than that of the full gap opening 19 . The observed finite density of states at E F is considered to originate from a metallic surface state, and this metallic surface state has been confirmed using electrical transport measurements (Iga-private communication). Moreover, a theoretical study has predicted that this metallic surface conductivity originates from topological SS 20 . However, the band structure of YbB 12 has not been observed using momentum-resolved measurements such as angle-resolved photoelectron spectroscopy (ARPES) because a well-defined clean surface has not been obtained (ARPES spectra at only two k-points have been reported in ref. 21).
In this article, we report a surface state (SS) on a clean surface of the KI YbB 12 (001) and its temperature-dependent reconstruction based on ARPES. We succeed in obtaining a clean YbB 12 surface which is suitable for detailed ARPES study. The SS is metallic and showed no dispersion along k z , indicating its surface localization. While the SS does not hybridize with the Yb 4f state lying just below the Fermi level (E F ) at room temperature, strong hybridization occurs at low temperatures. The reconstructed SS due to the c-f hybridization at 20 K is metallic and is continuously dispersed across the bulk bandgap of the KI between E F and B50 meV binding energy. This low-temperature SS behaviour agrees with the expected behaviour for SS on TKIs. Moreover, these results demonstrate the temperature-dependent holistic reconstruction of 2D states localized on the KI surface driven by the Kondo effect.

Results
Characterization of the YbB 12 (001) clean surface. Figure 1b shows the low-energy electron diffraction (LEED) pattern observed after the cleaning process (see Methods section). As shown by the sharp spots and low backgrounds, a well-ordered clean YbB 12 (001) surface was obtained. In addition to the integer order spots corresponding to a (001) in-plane lattice constant  (5.28 Å), we found fractional order spots showing c(2 Â 2) surface periodicity (Fig. 1b). The LEED pattern shows fourfold rotation symmetry, which is expected from the bulk crystal structure (Fig. 1a). Figure 1c shows the wide-valence band spectrum for the YbB 12 (001)-c(2 Â 2) surface taken at hn ¼ 80 eV. The Yb 2 þ and Yb 3 þ -4f levels are observed at similar energy positions to those measured with scraped or cleaved YbB 12 single crystals 21,22 . The major difference observed in this work is the absence of Yb 2 þ components around 0.9 and 2.2 eV, which are assigned to be surface components. It would be because the Yb atoms at the topmost surface are desorbed during the heating process. Indeed, as shown in Fig. 1d, we found a clear surface component at the B-1s level at the binding energy of 188 eV with a surface-sensitive condition (hn ¼ 280 eV, kinetic energy B90 eV), but this appeared as a weak tail in the bulk-sensitive measurement (hn ¼ 1,000 eV). Regarding the Yb 2 þ -4f levels, Fig. 1e shows almost the same peak positions with surface/bulk-sensitive conditions, supporting the above assumption that Yb atoms are not located at the topmost surface layer but in the deeper layers.   Figure 2b shows the intensity plots of the MDCs along the dashed line in Fig. 2a as a function of probing photon energies. As indicated by the dashed line, the MDC peak corresponding to the square EC does not change its in-plane wave vector, indicating that this state is a 2D surface state.  20 . We captured the bulk bands around the X point of bulk Brillouin zone. From the calculated bulk bands along G-X (see ref. 20), the highly dispersive conduction band clearly has its minimum at X; this means the bulk band dispersion around X is almost at the lower edge of the projected bulk bands in SBZ around G onto which the G-X line is projected. Below 100 meV, the S band dispersing is almost parallel to the calculated outer bulk band, which would be nearly parallel to the edge of the projected bulk bands. Note that S shows no dispersion along k z , which clearly differs from the bulk conduction band dispersing along the surface normal (see ref. 20). Such SS dispersion along the edge of the projected bulk bands are known for so-called Shockley-type SS on noble metal surfaces 23 and for surface resonances localized in the subsurface region of semiconductor surfaces 24 . This type of SS originates from bulk bands, but it is localized in the surface/subsurface region because of the truncation of the three-dimensional periodicity of the crystal. Some features of the ARPES plot, such as the inner bulk band below 100 meV and the number of 4f branches around G just below E F , does not agree with the calculation. This disagreement is discussed in the following part.
In addition to the highly dispersive S band, there is a less dispersive state around 30 meV (F in Fig. 2c), probably originating from the Yb 2 þ -4f bands. The F band appears as single peak at G (F 0 ) but splits to two branches (F up and F dn ) with the wave vector larger than 0.4 Å À 1 (smaller than À 0.4 Å À 1 ). These states cross with the S band around 0.3 Å À 1 where they apparently hybridize with each other. Such behaviour suggests c-f hybridization driven by the Kondo effect. The difference between the current case and other reported Kondo systems is that the hybridization occurs between SS, suggesting 2D c-f hybridization.
The nature of this c-f hybridization as well as the origin of the F band splitting dependence on k is examined in more detail in the following section.
Temperature-dependent reconstruction of SS. To examine the origin of the hybridization between the surface branches, we measured the temperature-dependent ARPES images at At 70 K, the dispersion is almost the same as that at 15 K, but the separation between the 4f branches is more diffuse than that at 15 K. At 190 K, S becomes a continuous metallic band across E F , and the 4f states almost disappear. On S, there is an undulation of the SS dispersion, which is possibly a precursor of the hybridization with the 4f states. At room temperature, the undulation of S is smaller but still visible. The overall evolution of surface bands indicates that hybridization between the highly dispersive S band and the almost-localized 4f states depends on the temperature, which is driven by the Kondo effect. This temperature-dependent behaviour, namely the disappearance of c-f hybridization at 190 K, agrees well with the previous reports about bulk states; the Kondo temperature of bulk YbB 12 is B220 K (ref. 22), where the c-f gap size converges to zero. In addition, the remaining undulation of S is also consistent with the mid-infrared peak that still survives at room temperature 18 . These results suggest a close relationship between the ARPES results and the bulk electronic states. However, Fig. 2b indicates the 2D nature of the S band. Thus, the F and F up/dn states intermixing with S should also be localized in the surface/subsurface region. One possible interpretation of this case is that the nature of the cf hybridization on the YbB 12 (001) surface is similar to that of the bulk bands.
Topological origin of SS. In addition to the states presented above, there is another state lying at E F as indicated by the white arrow in Fig. 3a. We focus on this state at low temperature in this section. Figure 4a,b shows the band dispersion along [100] taken at 16.5 and 53.5 eV, respectively. At both photon energies, a new state crossing E F at k //[100] B0.18 Å À 1 is clearly observed. As shown in Fig. 4d, this state is absent at room temperature and is replaced with another SS with dispersion that is almost parallel to the bulk c band; this SS is the same as that observed in Fig. 3d. This state is degenerate with the 4f (F) band at G. Moreover, this 4f band disperses between E F and 40 meV and becomes degenerate with the lower 4f branch (F dn ) at B0.85 Å À 1 ( M of the (1 Â 1) SBZ, see Fig. 4e). The complete SS dispersion exhibits a continuous connection across the Fermi level as well as the bulk c-f hybridization gap, whose size is at most 100 meV 18 , with two-fold degeneracy at high symmetry points of the (1 Â 1) SBZ. This metallic surface state can explain the remnant conduction path of YbB 12 observed at low temperatures (Iga-private communication). Note that no states corresponding with the metallic state observed by ARPES were observed in the bulk bands 17,18 .
The dispersion of the surface state observed here agrees with the expected behaviour for topological SS 1 : continuous dispersion across the bulk bandgap with Kramers degeneracy at the surface time-reversal invariant momentum. Indeed, the EC at E F taken with 16.5 eV photons indicates a closed Fermi contour surrounding G, one of the surface time-reversal invariant momentum on (001), as shown in Fig. 4c. This closed EC surrounding G agrees with the expected behaviour for SS with non-trivial topological order defined with time-reversal symmetry.
One of the most prominent characteristics of topological SS is the helical spin polarization. In other words, the electrons in such SS are spin polarized towards the direction perpendicular to both the wave vector k || and the surface normal. To elucidate such a feature, we have measured the circular dichroism (CD) of ARPES as shown in Fig. 5a. CD of ARPES can show the orbitalangular-momentum (OAM) polarization of the electronic state 25 . As depicted in Fig. 5b, the incident circularly polarized photons were in the (010) plane in our experimental geometry, and hence the helicity of the photons should probe the OAM polarization along [001] or [100] which is the helical direction explained above in the measurement plane along k || [010]. Figure 5a clearly shows the CD contrast around G in the second SBZ. The contrast around 0.2 Å À 1 at E F agrees with the metallic SS observed at k //[100] B0.18 Å À 1 in Fig. 4a,b. The sign of the contrast inverts with respect to G. Such behaviour agrees with what is expected for topological SS with helical spin polarization parallel/ anti-parallel to [100]. Moreover, spin-resolved photoelectron spectra shown in Fig. 5d-g clearly indicates the spin polarization (a-d) ARPES data are divided by the Fermi distribution function at each sample temperature convolved with the instrumental resolution. All data were taken along [110] with hn ¼ 16.5 eV. The intensity plots are symmetrized with respect to G (k ¼ 0 Å À 1 ) and shown in a colour scale: dark blue area represents high intensity. Circle (triangle) markers are the peak positions from ARPES momentum (energy) distribution curves (these curves are shown in Supplementary Fig. 2). The white arrow in (a) indicates a state lying at E F . parallel/anti-parallel to [100] around the Fermi level. Although the OAM polarization does not always correspond one-to-one to the spin polarization 26 , the spin-resolved spectra show that the CD contrast in Fig. 5a does correspond to the spin polarization of the metallic SS. These CD and spin-resolved ARPES results strongly suggest the helical spin polarization of the metallic SS around G on YbB 12 (001) observed in this work, which is the evidence of topological SS.
The non-trivial topological order defined with time-reversal symmetry, as suggested above, does not agree with the theoretical prediction based on LDA þ Gutzwiller method 20 which showed non-trivial mirror Chern number. It would be due to the accuracy limit of the calculation. Although the LDA þ Gutzwiller method can calculate the correlated electronic states much better than conventional LDA, the agreement with the experiment is not perfect. The topological order of YbB 12 can change in very small energy scale, the order of 10 meV, between the Yb-4f levels with different parities. Another cause of the disagreement is the surface atomic structure. As is explained with Fig. 1, the YbB 12 (001) surface in this work would be terminated by B atoms without Yb and forms c(2 Â 2) surface superstructure. In contrast, such surface atomic structure was not implemented to the DFT calculation. Although the surface atomic structure does not affect the topological order, the dispersion of the SS can drastically change accordingly 27 . Therefore, it is not so strange that there is a disagreement between ARPES and DFT. Actually, as shown in Fig. 2d, some calculated bulk bands based on LDA þ Gutzwiller method are not experimentally observed by ARPES. Following theoretical research about the discrepancy observed in this work might provide further insight into the surface electronic structure calculation with strong electron correlation.

Discussion
In summary, we discovered the new surface state on a clean surface of the YbB 12 (001) Kondo insulator and surveyed its temperature-dependent reconstruction using ARPES. The state is metallic and shows no dispersion along k z , indicating its surface localization. While the SS does not hybridize with the Yb-4f state lying just below the Fermi level (E F ) at room temperature, strong hybridization occurs at low temperatures. The reconstructed SS due to the c-f hybridization at 20 K is metallic and dispersed continuously across the bulk bandgap of the Kondo insulator between E F and the binding energy of B50 meV. This SS dispersion and spin/OAM polarization at low temperatures agree with the expected behaviour for SS on TKIs. Moreover, these results demonstrate the temperature-dependent holistic reconstruction of 2D states localized on the surface of the Kondo insulator driven by Kondo effect. Further study about quantitative spin polarization analysis about c-f hybridization would provide further insight into the topological order and electron correlation in the YbB 12 surface electronic structure.

Methods
ARPES and spin-resolved ARPES measurements. The ARPES measurements were performed with synchrotron radiation at the CASSIOPÉE beamline of the SOLEIL synchrotron, the BL7U beamline of UVSOR-III and the BL-2A MUSASHI beamline of the Photon Factory. The photon energies used in these measurements ranged from 15 to 1,600 eV. The incident photon is linearly polarized and the electric field of the photons lies in the incident plane (so-called p polarization) for the measurements shown in Figs 1-4 and circularly polarized for Fig. 5. The photoelectron kinetic energy at E F and the overall energy resolution of each ARPES set-up (B20 meV for ARPES and B80 meV for wide-valence spectra shown in Fig. 1d,e) were calibrated using the Fermi edge of the photoelectron spectra from Ta foils attached to the sample. Spin-resolved ARPES measurements were performed at HiSOR BL9B with linearly polarized photons at 50 eV. The energy resolution was 80 meV and the effective Sherman function of the spin detector was set to 0.3. The acceptance angle for the spin detector was ± 1.5°.
Sample preparation. Single crystalline YbB 12 was grown via the floating-zone method using an image furnace with four xenon lamps 17 . The crystal was cut with a diamond saw along the (001) plane based on an in-situ Laue pattern and was then polished in air until a mirror-like surface plane was obtained. The polished YbB 12 (001) crystal was heated to 1650 K in ultra-high vacuum chambers for B10 s. For heating, a SiC wafer was underlaid below YbB 12 (001); heating the SiC wafer with direct current simultaneously heats the attached YbB 12 .
Data availability. The data supporting the findings of this study are available within the article and its Supplementary Information, or from the authors upon request. [010] [010]