Breakdown of bulk-projected isotropy in surface electronic states of topological kondo insulator smb6(001)

ABSTRACT The topology and spin-orbital polarization of two-dimensional (2D) surface electronic states have been extensively studied in this decade. One major interest in them is their close

relationship with the parities of the bulk (3D) electronic states. In this context, the surface is often regarded as a simple truncation of the bulk crystal. Here we show breakdown of the

bulk-related in-plane rotation symmetry in the topological surface states (TSSs) of the Kondo insulator SmB6. Angle-resolved photoelectron spectroscopy (ARPES) performed on the vicinal

SmB6(001)-_p_(2 × 2) surface showed that TSSs are anisotropic and that the Fermi contour lacks the fourfold rotation symmetry maintained in the bulk. This result emphasizes the important

role of the surface atomic structure even in TSSs. Moreover, it suggests that the engineering of surface atomic structure could provide a new pathway to tailor various properties among TSSs,

such as anisotropic surface conductivity, nesting of surface Fermi contours, or the number and position of van Hove singularities in 2D reciprocal space. SIMILAR CONTENT BEING VIEWED BY

OTHERS HIDDEN BULK AND SURFACE EFFECTS IN THE SPIN POLARIZATION OF THE NODAL-LINE SEMIMETAL ZRSITE Article Open access 17 March 2021 TWO-DIMENSIONAL HEAVY FERMION IN A MONOATOMIC-LAYER KONDO

LATTICE YBCU2 Article Open access 01 December 2023 RICH NATURE OF VAN HOVE SINGULARITIES IN KAGOME SUPERCONDUCTOR CSV3SB5 Article Open access 25 April 2022 INTRODUCTION The close

correspondence between symmetry operations in 3D bulk bands and the topological character of the surface states lying on the edge of a crystal has been one of the central topics of solid

state physics in this decade1. Such topological surface states (TSSs) are attractive not only for basic science but also for spintronic applications due to their momentum-dependent

spin–orbital polarization2,3. Since TSSs originate from the topological order of bulk states, some qualitative characteristics of TSSs, such as the metallic band dispersion across the bulk

bandgap, are robust against any non-magnetic external perturbations as long as the bulk states remain unchanged. This is a strong point on the one hand because of the expected

contamination-tolerant working of devices, for example. On the other hand, the role of the surface atomic structure in TSSs is regarded as rather unimportant because of the robustness. Some

theoretical and experimental studies reported modification of TSSs by surface treatments, such as surface oxidization4, chemical or photochemical ageing5,6, and a small interlayer rotation

forming a moiré modulation on the surface7. However, such previous works were focused on how to perturb the pristine TSS. Actually, the unit cells of the surface lattice in these works were

always the same length of basis vectors as the ideally truncated bulk crystal, with the symmetry operations obtained by simple projection of bulk 3D space group. Some studies focused on

topological electronic states localized at 1D edges or hinges, but they still suppose the similar simple projection from 3D to 1D systems8,9. Although some drastic electronic phenomena, such

as 1D charge-density-wave formation on 2D semiconductor surfaces10, obtained by forming a surface atomic structure independent of the substrate, are already known, the role of the surface

superstructures in TSSs has not been studied in detail yet, to the best of our knowledge. Samarium hexaboride (SmB6) is a long-known Kondo insulator, in which a bulk bandgap opens at low

temperature because of the Kondo effect11. It is the first material proposed as a candidate for topological Kondo insulators (TKIs), and it hosts a metallic TSS coexisting with strong

electron correlation12,13 and was recently confirmed as a TKI by angle-resolved photoelectron spectroscopy (ARPES) experiments after a long debate14,15,16,17,18, as summarized in ref. 19.

The (001) surface of SmB6 is also known as a valuable example of a well-defined surface superlattice among TIs. Although cleavage provides multiple surface terminations20, in situ surface

preparation, typically by the cycling of Ar ion sputtering and annealing, results in an uniform surface superstructure such as (1 × 2) and (2 × 2)14,21,22, making the SmB6(001) surface a

good template to study the role of the surface atomic structure in TSSs. The remaining barrier for such research is that the obtained SmB6(001) surfaces have two or more equivalent domains

coexisting with nearly the same area. For example, double-domain (1 × 2) and (2 × 1) surfaces could provide apparent fourfold rotation symmetry of the TSS by overlapping of two twofold

domains rotated 90° to each other, as observed on the Si(001) surface23. In this work, we show the TSS on the uniform and semi-single-domain SmB6(001)-_p_(2 × 2) surface prepared in situ.

One surface domain is dominantly grown by using a vicinal (001) substrate, confirmed by low-energy electron diffraction (LEED). The dispersion and orbital–angular-momentum (OAM) polarization

of the SmB6(001) TSS is observed by ARPES without ambiguity from the multidomain overlap for the first time. The ARPES data show that the TSS is anisotropic and that the Fermi contour (FC)

lacks the fourfold rotation symmetry that is maintained in bulk. This result emphasizes the important role of the surface atomic structure even in the TSS. RESULTS VICINAL (001) SURFACE OF

SMB6 As depicted in Fig. 1a, the bulk-truncated (001) surface of SmB6 has a fourfold rotation symmetry. After cycles of Ar ion sputtering and annealing (see “Methods” for details), the

vicinal SmB6(001) surface exhibited the LEED patterns shown in Fig. 1b. In contrast to most of the earlier studies reporting (2 × 1) surface periodicity14,21, the (1/2 1/2) fractional spot

indicated the _p_(2 × 2) surface structure at the primary electron energy (_E_p) of 65 eV. Moreover, other fractional spots at _E_p = 45 eV, (1 − 1/2) and (1/2 − 1), show different

intensities from each other, although they should be identical if the surface has fourfold rotation and time-inversion symmetries. Note that different diffraction spots become bright at _E_p

 = 45 and 65 eV simply because to sweep LEED _E_p corresponds to sweep the size of the Ewald sphere in reciprocal space. The asymmetric intensities between (1 – 1/2) and (1/2 – 1) are

quantitatively shown by the LEED line profiles in Fig. 1c. This shows that the obtained surface has an anisotropic atomic structure without fourfold rotation symmetry. The line profile also

shows that this surface hosts the mirror planes [100] and [010], since the spots (1 ± 1/2) have nearly the same heights. Note that the height difference between (1 − 1/2) and (1/2 − 1) does

not directly reflect the area ratios of surface domains; the obtained surface periodicity is _p_(2 × 2), and thus both (1 − 1/2) and (1/2 − 1) spots could appear even from the perfect

single-domain surface. Figure 1d shows the B 1_s_ core level and Sm2+ 4_f_ valence bands obtained from angle-integrated photoelectron spectra of SmB6(001)-_p_(2 × 2). Different from the

cleaved SmB6(001) cases17, we found no clear “surface” term which appears at different energies from the main peaks. This would occurs because the heating process during the surface

preparation removes the metastable Sm and B atoms which are the origin of the “surface” terms. The B 1_s_ peak has a tailed shape with respect to higher kinetic energies, suggesting that

some boron atoms are in a different surrounding environment from the bulk case, but the difference is not as drastic as in the "boron-terminated” case of the cleaved surfaces17,20. This

suggests that small displacements of the surface boron atoms are the origin of the _p_(2 × 2) superlattice. While some cleaved surfaces of SmB6(001) were reported to be inhomogeneous with

various termination atoms17,20,24, we found no such signature from the current surface. Further discussion on this point is shown in Supplementary Note 1. Based on these results, we propose

a possible model of _p_(2 × 2) surface superstructure, as illustrated in Fig. 1e and f. In this model, no surface defects nor adatoms are supposed, and the _p_(2 × 2) superlattice is formed

only by displacements of B6 and Sm atoms at the topmost two atomic layers. Such picture agrees with the less drastic change of surrounding conditions of the surface atoms, which was

suggested by the core-level spectra explained above. In addition, the number of neighboring atoms of the displaced Sm is the same as those in bulk, in contrast to the reduction for the

topmost B6. It rationalizes the core-level spectra showing the "surface” term only for boron peaks. Note that this model is just a possible example to satisfy what were observed by LEED

and core-level spectra. Further experiments are required to determine the surface atomic structure accurately, such as dynamical LEED analysis25 or Weissenberg reflection high-energy

electron diffraction26, while the _p_(2 × 2) surface unit cell without fourfold rotation symmetry is enough for the following discussion in this article. TSS OF THE VICINAL SMB6(001)-_P_(2 ×

 2) SURFACE Figure 2a shows the FCs around the Fermi level (_E_F) measured with circularly polarized photons at 35 eV. The spectra obtained by using both right- and left-handed polarizations

are summed to avoid the anisotropic intensity distribution due to the circular dichroism (CD). Figure 2b shows a schematic drawing of the obtained FCs S1, S2, and S3. The oval enclosing

\(\bar{{{{{{{{\rm{X}}}}}}}}}\) (S1) has a similar shape to those observed in the earlier studies15,16,17,19,21. The stark contrast to the earlier studies is that the FC around the other

\(\bar{{{{{{{{\rm{X}}}}}}}}}\) point, S1’ depicted in Fig. 2b, is quite weak, although they should be identical, if the surface has a fourfold rotation symmetry. To highlight this

difference, the other \(\bar{{{{{{{{\rm{X}}}}}}}}}\) point is named as \(\bar{{{{{{{{\rm{Y}}}}}}}}}\) (Fig. 2a). One possibility to explain this anisotropy is the ARPES experimental

geometry. However, as illustrated in Fig. 2c, the ± _k__y_//[010] orientations are identical to each other, even when the photoelectron incidence orientation is taken into account. Moreover,

S1’ becomes as evident as S1 near the edge of the crystal surface where the vicinal miscut is expected to be different from that at the center of the polished surface, indicating that the

difference between S1 and S1’ is from the surface domains (ARPES data are shown in SM). Together with the anisotropic LEED patterns (Fig. 1b, c), the faint S1’ can reasonably be assigned to

the minor-area domains and to the fact that the SmB6(001)-_p_(2 × 2) surface lacks the fourfold rotation symmetry with the S1 FC only around one \(\bar{{{{{{{{\rm{X}}}}}}}}}\) point. The

other FCs enclosing \(\bar{{{\Gamma }}}\), S2 and S3, are also clearly observed, in contrast to the blurred FCs in earlier works16. This is due to the uniform single-domain surface

preparation over a wide area of the sample. The shape of S2 is similar to that observed on the cleaved (001) surface. While that state was claimed as the umklapp of S1 by (1 × 2) surface

periodicity at first17, this assignment has not yet reached a consensus, as the following discussion made a counterargument on this assignment19. On the other hand, as shown in Fig. 2a and

b, the shapes of S1 and S2 observed here are clearly different, indicating that S2 is another, independent FC. All the three FCs observed here lacks the fourfold symmetry, as shown in Fig. 

2. Such breakdown of the bulk-related symmetry in the TSS is observed for the first time among TIs, to the best of our knowledge. It should be derived from the anisotropic surrounding

conditions of Sm atoms near the surface, since the bulk states around the Kondo gap is mainly derived from Sm 4_f_ and 5_d_ orbitals. Such condition can be naturally satisfied by assuming

_p_(2 × 2) surface superstructure; for example, minor displacements of Sm below the topmost surfaces as depicted in Fig. 1f. On the other hand, no folding of FCs at the SBZ boundary was

observed, while it is rather common case among surface states with superstructure, as discussed in Supplementary Note 2. Figure 3 shows the band dispersions near _E_F. The almost localized

Sm 4_f_ band lies slightly below _E_F (~20 meV) and the Sm 5_d_ bands disperses in 150–50 meV, reflecting the itinerant character. Around the crossing point between them, the bands bend,

indicating the _c_-_f_ hybridization induced by the Kondo effect. Above the Sm 4_f_ band, the metallic bands continuously disperses between _E_F and Sm 4_f_ in Cuts 1–3. Their Fermi

wavevectors (_k_F) are consistent with the FCs observed in Fig. 2. Note that distinguishing S1, S2 and S3 in Fig. 3b is difficult because they overlap with each other at _E_F along this

orientation. While the surface bands corresponding to S2 and S3 are not very clear from the 2D intensity plot in Fig. 3c, this is because of the too strong Sm 4_f_ band and the momentum

distribution curve (MDC) at _E_F shows distinct peaks corresponding to them. Moreover, Fig. 3d shows the dispersion of S2 and S3 close to _E_F without such difficulty. This is thanks to the

photon energy (18 eV) for Fig. 3d, where the photoemission cross-section for Sm 4_f_ becomes small. The _k_F values for S2 and S3 obtained in Fig. 3c and d show no difference depending on

the photon energy, indicating that their 2D nature arises from the surface. For further confirmation, we also checked the lack of 3D dispersion for S2 and S3 by measuring a series of MDCs at

_E_F with different photon energies (see Supplementary Fig. 2 in SM). OAM POLARIZATION OF THE TSS One of the most prominent characteristics of TSSs is the helical spin and OAM polarization,

which is always perpendicular to the in-plane wavevector1. Figure 4 shows a CD-ARPES map corresponding to the region shown in Fig. 3. The CD of ARPES reflects the OAM polarizations

projected onto the photon-incident orientation. As illustrated in Fig. 2c, CD in the current experimental geometry corresponds to OAM polarization along the in-plane and normal to _k__y_, or

out-of-plane orientation. Figure 4a shows that the oval-shaped S1 around \(\bar{{{{{{{{\rm{X}}}}}}}}}\) has helical OAM polarization consistent with the earlier CD-ARPES15 and spin-resolved

ARPES16 results. Figure 4b and c show that the surface bands S2 and S3 also have OAM polarizations whose sign inverts from +_k__y_ to −_k__y_, obeying the time-inversion symmetry. This

behavior, helical OAM polarizations with time-reversal symmetry, is consistent with what is expected for TSSs1,19. Figure 4d illustrates the OAM polarizations of each FC, assuming that they

are parallel to the helicities of the incident-photon polarizations: parallel (anti-parallel) to the photon-incidence vector for right- (left-) handed polarization. According to this, the

helicities of the OAM polarizations for S1 (counterclockwise) are opposite to those for S2 and S3 (clockwise). Such behavior is not expected from the analytical calculation with the winding

number27. However, note that the sign of the CD-ARPES signal is not suitable information to be directly compared with such calculation of the initial states. First, it is easily affected by

the photoelectron excitation process28. Second, the calculation does not include the surface atomic structure obtained in this work. Finally, TSSs were recently revealed to often contain

multiple wavefunction components with different orbital and spin polarizations even at single (_E_, _k_) point; thus, the polarization of photoelectrons is not always the direct information

of the initial state29,30. Therefore, further datasets, especially spin-resolved ARPES with multiple incident-photon energies and polarizations, are required to conclude the winding number

of the TSS. DISCUSSION We have revealed that the TSS of SmB6(001)-_p_(2 × 2) is highly anisotropic. From this anisotropy, the other electronic properties, such as the electron conductivity

and net spin polarization via the surface currents, are also suggested to be anisotropic on SmB6(001)-_p_(2 × 2), as far as they are derived from the TSS. Note that none of these properties

are topologically protected. Therefore, examining the rotation asymmetry from the vicinal SmB6(001) sample with in situ surface preparation would be an interesting new pathway to distinguish

the origin and dimensionality (2D or 3D) of unconventional electronic phenomena observed in SmB6, such as the thermodynamic properties31 and quantum oscillations32,33,34,35,36,37. If one

could apply the surface preparation method similar to ours to vicinal SmB6(001) sample and then insert it to a magnet equipment for de Haas van Alphen oscillation measurements without

breaking the vacuum environment, such experimental setup would provide conclusive evidence about the role of surface on the quantum oscillation. Since the folding of FCs by surface

superstructure changes the apparent shape of FCs drastically, one could have a question about its role on topological order. In most cases including SmB6(001)-_p_(2 × 2), surface

superstructure causes no change the energetic order of bulk bands nor magnetic order. Therefore, there shouldn’t be any change in topological order before and after the formation of surface

superstructure. However, it would be helpful to discuss how to determine the topological order with the surface superstructure, since it is often determined by counting the number of FCs to

be odd or even, around surface time-reversal invariant momenta (TRIM); \(\bar{{{\Gamma }}}\), \(\bar{{{{{{{{\rm{X}}}}}}}}}\), \(\bar{{{{{{{{\rm{Y}}}}}}}}}\), and

\(\bar{{{{{{{{\rm{M}}}}}}}}}\) for SmB6(001)18,19,38. For this counting, we propose to double check the number of FCs both by using (1 × 1) bulk-truncated SBZ as well as that with folding

according to the surface superstructure. Circled numbers in Fig. 4d and e are examples of this method applied to SmB6(001)-_p_(2 × 2), showing 3 FCs, odd number consistent with the

non-trivial topological order18,19. Note that S1 at the bottom side of Fig. 4d is identical to the top one because of the translational symmetry, and thus it should not be included to this

FC counting. This method emphasizes the importance to prepare the single-domain surface to discuss the topological order of unknown material; for example, surface Dirac cones doubled by two

nonequivalent surface terminations, as observed in ref. 39, could derive false counting of FCs. The folding of TSS by surface superstructure could play further role on the unconventional

electronic phenomena of TSS. It duplicates FCs formed by TSS, making the additional crossing points with van-Hove singularity (VHS, arrows in Fig. 4f). Such VHS formation is discussed

theoretically based on a moiré modulation to expect enhanced topological superconductivity40. Moreover, this work exhibited that the surface superstructure distorts surface FCs at the same

time. It suggests that engineering of surface superstructure could tailor the number and position of VHS in the reciprocal space as well as the other parameters of FCs, such as nesting

vector dominating surface density-wave formation41. Actually, the observed FC on SmB6(001)-_p_(2 × 2) does exhibit triple degenerate points of TSSs as guided by arrows in Fig. 4e. On the

other hand, the reconstruction of TSS in Kondo gap observed here is the first case, to the best of our knowledge. In most cases, surface superstructure are regarded to play a major role in

larger energy scale typically in 0.1–1 eV, orders of magnitude larger than those of Kondo gap (a few tens of meV). The VHSs formed by surface superstructure possibly also enhance the

electron correlation effect expected to TSS of TKI, such as the emergence of heavy surface states and non-Hermitian exceptional points42,43. From these perspectives, detailed electron

behavior in smaller energy and temperature scale, in orders of few meV and Kelvins, respectively, of SmB6(001)-_p_(2 × 2) would be an encouraging test peace to examine the role of the

surface superstructure on TKI. METHODS SAMPLE PREPARATION Single crystalline SmB6 was grown by the floating-zone method by using an image furnace with four xenon lamps21,44. The sample cut

along the (001) plane was mechanically polished in air with a small angle offset toward [010] until a mirror-like shiny surface was obtained with only a few scratches when observed under an

optical microscope (multiple ×10 magnification). The miscut angle is estimated to be ~ 1° from the side-view images obtained by the optical microscope. The polished sample was moved to

ultra-high-vacuum (UHV) chambers and cleaned in situ by repeated cycles of Ar ion sputtering (1 keV) and annealing up to 1400 ± 50 K. The cleaned surface was transferred to the measurement

chambers for LEED or ARPES without breaking the UHV. LEED MEASUREMENTS The LEED measurements were performed by using a conventional electron optics (OCI, Model BDL800IR) at beamline 7U of

UVSOR-III. The sample was mounted on a homemade 6-axis goniometer maintained at 100 K. The electron incident angle was adjusted to be parallel to the surface normal ([001]) by using the

rotation angles of the goniometers. ARPES EXPERIMENTAL SETUP The ARPES measurements were performed with synchrotron radiation at the CASSIOPÉE beamline of synchrotron SOLEIL. The photon

energies used in these measurements ranged from 18 to 240 eV. The polarization of incident photons is depicted in Fig. 2c, including linear polarization with the electric field lying in the

incident plane (H) and circular polarizations (R and L). The photoelectron kinetic energy at _E_F and the overall energy resolution of the ARPES setup ( ~ 15 meV) were calibrated using the

Fermi edge of the photoelectron spectra from Ta foils attached to the sample. DATA AVAILABILITY The datasets generated and/or analyzed during this study are available from the corresponding

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acknowledge W. Breton and F. Deschamps for their support during the experiments on the CASSIOPÉE beamline at the SOLEIL synchrotron. We also thank S. Ideta and K. Tanaka for their support

for LEED measurements at UVSOR with proposal No. 20-784. The ARPES experiments were performed under SOLEIL proposal No. 20191629. This work was also supported by JSPS KAKENHI (Grants Nos.

JP20H04453, JP19H01830, and JP20K03859). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * National Institutes for Quantum Science and Technology, Sendai, 980-8579, Japan Yoshiyuki Ohtsubo *

Graduate School of Frontier Biosciences, Osaka University, Suita, 565-0871, Japan Yoshiyuki Ohtsubo, Takuto Nakamura & Shin-Ichi Kimura * Department of Physics, Graduate School of

Science, Osaka University, Toyonaka, 560-0043, Japan Yoshiyuki Ohtsubo, Toru Nakaya, Takuto Nakamura & Shin-Ichi Kimura * Synchrotron SOLEIL, L’Orme des Merisiers, Départementale 128,

F-91190, Saint-Aubin, France Patrick Le Fèvre & François Bertran * Graduate School of Science and Engineering, Ibaraki University, Mito, 310-8512, Japan Fumitoshi Iga * Institute for

Molecular Science, Okazaki, 444-8585, Japan Shin-Ichi Kimura Authors * Yoshiyuki Ohtsubo View author publications You can also search for this author inPubMed Google Scholar * Toru Nakaya

View author publications You can also search for this author inPubMed Google Scholar * Takuto Nakamura View author publications You can also search for this author inPubMed Google Scholar *

Patrick Le Fèvre View author publications You can also search for this author inPubMed Google Scholar * François Bertran View author publications You can also search for this author inPubMed

 Google Scholar * Fumitoshi Iga View author publications You can also search for this author inPubMed Google Scholar * Shin-Ichi Kimura View author publications You can also search for this

author inPubMed Google Scholar CONTRIBUTIONS Y.O. conducted the ARPES experiments with assistance from P.L.F. and F.B., Y.O., T. Nakaya, and T.Nakamura performed the LEED experiments. F.I.

grew the single-crystal samples. Y.O. and S.-i.K. wrote the text and were responsible for the overall direction of the research project. All authors contributed to the scientific planning

and discussions. CORRESPONDING AUTHORS Correspondence to Yoshiyuki Ohtsubo or Shin-Ichi Kimura. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. PEER

REVIEW PEER REVIEW INFORMATION _Nature Communications_ thanks James Allen, and the other, anonymous, reviewer for their contribution to the peer review of this work. Peer reviewer reports

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and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Ohtsubo, Y., Nakaya, T., Nakamura, T. _et al._ Breakdown of bulk-projected isotropy in surface electronic states of topological Kondo

insulator SmB6(001). _Nat Commun_ 13, 5600 (2022). https://doi.org/10.1038/s41467-022-33347-0 Download citation * Received: 12 July 2022 * Accepted: 12 September 2022 * Published: 23

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