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## Creator

Yuto Fukushima, Kaishu Kawaguchi, [Kenta Kuroda](https://orcid.org/0000-0002-0151-0876), [Masayuki Ochi](https://orcid.org/0000-0001-7438-4797), Motoaki Hirayama, [Ryo Mori](https://orcid.org/0000-0002-8684-9421), [Hiroaki Tanaka](https://orcid.org/0000-0002-5178-7777), [Ayumi Harasawa](https://orcid.org/0000-0002-2455-4863), Takushi Iimori, Zhigang Zhao, [Shuntaro Tani](https://orcid.org/0000-0003-0608-7410), [Koichiro Yaji](https://orcid.org/0000-0002-0721-1316), Shik Shin, [Fumio Komori](https://orcid.org/0000-0002-6405-4177), [Yohei Kobayashi](https://orcid.org/0000-0002-9959-566X), [Takeshi Kondo](https://orcid.org/0000-0002-3912-5172)

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©2024 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Spin-polarized saddle points in the topological surface states of elemental bismuth revealed by pump-probe spin- and angle-resolved photoemission spectroscopy](https://mdr.nims.go.jp/datasets/0f4af390-9f2f-461c-aa60-cbef70ab68cb)

## Fulltext

Spin-polarized saddle points in the topological surface states of the elemental Bismuthrevealed by a pump-probe spin-resolved ARPESYuto Fukushima,1 Kaishu Kawaguchi,1 Kenta Kuroda,2, 3 Masayuki Ochi,4, 5Hiroaki Tanaka,1 Ayumi Harasawa,1 Takushi Iimori,1 Zhigang Zhao,1, 6 Shuntaro Tani,1Koichiro Yaji,7 Shik Shin,8 Fumio Komori,1 Yohei Kobayashi,1 and Takeshi Kondo1, 91Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan2Graduate School of Advanced Science and Engineering,Hiroshima University, Higashi-hiroshima, Hiroshima 739-8526, Japan3International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SCKM2),Hiroshima University, Higashi-hiroshima, Hiroshima 739-8526, Japan4Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan.5Forefront Research Center, Osaka University, Toyonaka, Osaka 560-0043, Japan.6School of Information Science and Engineering, Shandong University, Qingdao, 266237, China7Research Center for Advanced Measurement and Characterization,National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0003, Japan8Office of University Professor, The University of Tokyo, Kashiwa, Chiba 277-8581 Japan9Trans-scale Quantum Science Institute, The University of Tokyo, Tokyo 113-0033, Japan(Dated: April 3, 2023)We use a pump-probe, spin-, and angle-resolved photoemission spectroscopy (ARPES) with a10.7 eV laser accessible up to the Brillouin zone edge, and reveal for the first time the entire bandstructure, including the unoccupied side, for the elemental bismuth (Bi) with the spin-polarizedsurface states. Our data identify Bi as in a strong topological insulator phase (Z2=1) against theprediction of most band calculations. We unveil that the unoccupied topological surface states pos-sess spin-polarized saddle points yielding the van Hove singularity, providing an excellent platformfor the future development of opto-spintronics.Prototype Z2 topological insulators (TIs) are Bi2Se3and Bi2Te3 for strong TIs [1–3] and β-Bi4I4 [4–6] andBi14Rh3I9 [7–9] for weak TIs, which all contain Bi withstrong spin-orbit interaction. Bi is, thus, the most pop-ular element for a material design realizing topologicalphases. Surprisingly, however, the bulk topology of theelemental Bi itself has not yet been identified and con-tinues to be debated [10–16], even though its properties,including spin-polarized surface states, have been vigor-ously investigated for so many years [17, 18, 20–23]. Re-cently, a possible higher-order topological state has beensuggested for the bulk Bi by extending the topologicalclassification to Z4 [24, 25]. However, it is on the basisthat Bi is topologically trivial (Z2=0) within the Z2 in-dex. Therefore, identifying the actual topological phasein the elemental Bi is getting more crucial in condensedmatter physics.The bulk topology of Bi can be experimentally deter-mined by identifying how two surface bands (SS1 andSS2) are connected into the bulk conduction and valencebands (BCB and BVB) around M, as represented in Fig.1. Despite these simple criteria, there are several reasonsas follows for having this issue still controversial:(1) High-quality Bi is commonly prepared as films. Bifilms get free-standing around 15 BLs (6 nm) [26], andstress from a substrate is totally removed when thickerthan ∼25 BLs (∼10 nm) [27]. However, an interactionbetween the front and back surface states even in rel-atively thick films as 200 BLs may open a gap in thesurface states and mislead the bulk topology [13, 15, 28].(2) The entire band structure should be determinedby experiments for a fair comparison with band calcula-tions. However, this cannot be accomplished by a stan-dard ARPES observing only the occupied states. Oneway of visualizing the unoccupied band is to raise thesample temperature and detect thermally excited elec-tronic states above the Fermi level (EF). However, theoriginal bulk topology might be altered by lattice expan-sion inevitable at high temperatures [29, 30].(3) The bulk band gap around M is so small (∼15meV), making it hard to clarify the connections of surfacebands to the bulk bands [31, 32].In this Letter, we overcome all these difficulties andclarify the genuine topological state in the elemental Bi.Following are our solutions (s1)-(s3) to (1)-(3):(s1) We prepare a film of ∼1000 BLs (∼0.4 µm), whichis, according to theory [15], thick enough to make theoverlap of wavefunction between the front and back sur-face states negligible.(s2) We use a pump-probe spin-ARPES we recentlydeveloped, and unveil the band structure including theunoccupied states over the entire Brillouin zone (BZ).Importantly, this technique allows observing unoccupiedstates without raising the lattice temperature by takingdata just after pumping.(s3) We employ spin-resolved spectra, which can dis-tinguish between the surface and bulk bands with andwithout the spin polarization, respectively, to identifyarXiv:2303.17816v1  [cond-mat.mtrl-sci]  31 Mar 20232?(a) (b) (c)EFSS1SS2(d) non-trivial (e) trivial (f) trivial (g) trivial1BLFIG. 1. (a) Crystal structure of Bi in the (111) orientation.(b) Brillouin zone for bulk and (111) surface. (c) Schematicband structure along Γ − M direction on the Bi(111) surface.Blue and red lines show the surface bands (SS1 and SS2) within-plane spin polarization in opposite directions. (d)-(g) Allpossible relationships between surface and bulk bands aroundM corresponding to different bulk topologies. [11]whether each of the two surface bands is connected tothe conduction band or the valence band.These experiments conclusively identify the bulk bandtopology of the elemental Bi to be non-trivial (Z2=1).The state-of-the-art spin-ARPES further reveals a uniquefeature in the unoccupied surface band: spin-polarizedsaddle points that form a hexagonal helical spin textureand generate the van Hove singularity (vHS) in the den-sity of states. This could be an iconic structure for thefuture opto-spintronics application with Bi, which con-trols the spin current by photoexcitation [33–37].Single-crystal Bi(111) films of ∼1000 BL (∼0.4 µm)were prepared in situ by depositing Bi on an Si(111)7 × 7 surface (see more details in supplementally mate-rials). All ARPES measurements were performed with a10.7 eV laser generated by a home-built Yb:fiber pulselaser [38, 39]. The fundamental Yb:fiber laser (1.19 eV)was also used as a pump light. The energy resolutionwas ∼20 meV and ∼25 meV for pump-probe ARPESand pump-probe SARPES, respectively. The time reso-lution was 360 fs. We used a mild pump (0.08 mJ/cm2)preventing a lattice vibration. The high repetition rateof the laser (1MHz) and a high-efficiency spin-detector(VLEED) enabled us to obtain a sufficient count rate ofspin signals. All experiments were performed around 70K using p-polarized light for both the pump and probe.Details about our newly developed ARPES system willbe discussed elsewhere [19].First, we investigate the spin-integrated band struc-ture of Bi(111). Figures 2(a) and 2(b) plot the Fermisurface map and the occupied band dispersion along Γ −M measured without pumping. We confirm well-knownsurface bands: a hexagonal electron pocket around Γ,petal-like hole pockets surrounding it, and an elongatedelectron pocket around M [20, 21]. These are formedby two surface bands (SS1 and SS2) connecting to bulkE − EF (eV)0.20-0.2(b)0.80.40-0.40.20-0.2kx (Å-1)(c)-0.1 0 0.10.30.20.1E − EF (eV)ky (Å-1)(e) (f)0.80.40-0.4-0.200.2k y (Å-1 ) (a)kx (Å-1)-0.200.2-0.200.2-0.200.2-0.200.2-0.200.2-0.2 0 0.2-0.200.2kx (Å-1)(d)k y (Å-1 )E − EF  (eV)0.250.200.150.100.050FIG. 2. Band structures of Bi revealed by pump-probeARPES. (a) Fermi surface map. (b,c) Band dispersion alongΓ − M measured without and with pump. (d) Energy con-tour maps on the unoccupied side from 0 to 0.25 eV. (e) Banddispersion crossing the saddle point along ky. (f) Schematicof spin-polarized saddle points with a hexagonal structure.Magenta arrows in (c,d,e) indicate the saddle point.bands around Γ and M. We further perform the pump-probe measurements and successfully visualize the bandsup to the unoccupied side [Fig. 2(c)].Figure 2(d) displays the contour energy maps at dif-ferent binding energies on the unoccupied side. In-terestingly, we find that hexagonal and petal-likepockets, which are detached from each other aroundE − EF = 0.15 eV, get closer with increasing binding en-ergy. They touch with each other around 0.2 eV (pointedby a magenta arrow) and eventually turn to continuousparallel segments of an enlarged energy contour (see theregions of dotted light blue rectangles). The touchingpoint locates at the top of the upward energy dispersionalong Γ − M [arrow in Fig. 2(a)] as well as at the bot-tom of the downward energy dispersion perpendicular tothe Γ − M cut as exhibited in Fig. 2(e). Therefore,this energy state [arrows in Figs. 2(a), 2(d), and 2(e)]is a saddle point, which forms the van Hove singularityin the density of states [40, 41]. The same saddle pointis placed at six locations in the surface BZ [Fig. 2(f)],which forms a helical spin structure, as revealed below.The spin polarization is investigated by pump-probespin-ARPES. Figure 3(b) plots the in-plane Y component3of spin polarization (SY ) for the orange rectangular re-gion in Fig. 2(a). Thanks to the pump-probe technique,the spin-polarized states of surface bands (SS1 and SS2)are unveiled not only on the occupied side but also on theunoccupied side. Notably, the sign reversal of spin be-tween SS1 and SS2 is clearly exhibited. Importantly, ourexperiments demonstrate that the saddle points yieldingthe vHS around 0.2 eV are spin-polarized with a helicalspin structure, as illustrated in Fig. 2(f). This furtherimplies that massive spin currents can be controlled byphotoexciting these states with circularly polarized mid-infrared light.We estimate |SY | for the upper and lower surface bandsalong Γ - M in Fig. 3(a) to examine how the spin-polarized surface states are mixed with or absorbed intothe bulk states without spin-polarization. The spin po-larization should be observed as 100% for the surfacestates if the following two conditions are fulfilled [42].One is that the E-k points are far from the time-reversalinvariant momenta (Γ and M) at which the up and downspins inevitably degenerate. Second is that they are freefrom hybridization with the bulk states which reducesspin-polarization. As expected, while SY ’s of SS1 andSS2 are close to 100% in the momentum range far fromΓ and M (0.2 Å−1< kx < 0.6 Å−1), these decrease andeventually become almost zero at Γ and M. Neverthe-less, we find a clear difference between SY (kx)’s of theupper and lower surface bands: the latter decreases morerapidly than the former with approaching Γ and M wherethe valence bands are situated, as represented by blue ar-rows in Fig. 3(a). This indicates that the lower surfaceband is absorbed to (or hybridized with) the balk bandsextensively around Γ and M.Since the spin-polarization signals originate from thesurface states, the surface bands can be determined sep-arately from the bulk states by tracing the peak posi-tions of the spin-polarized spectra. In particular, wemeasured the spin-polarization map with high precisionfor the bands around M [Fig. 3(c)], which is the keymomentum region to determining the bulk topology ofBi. Figure 3(d) plots spin-resolved energy distributioncurves (EDCs) at k’s marked by arrows in Fig. 3(c). Thespin-integrated EDCs (black lines) are also superposed.Although peaks are observed for the upper surface bandslightly below EF, only a hump structure, poorly definedas a quasiparticle, is obtained for the lower surface bandaround −0.1 eV. This agrees with our assertion that thelower surface band is significantly hybridized with thebulk valence band around M with a broad spectral con-tinuum; the bulk state is observed as a continuum pro-jected onto the surface due to the kz broadening typicalfor ARPES, which is a surface-sensitive technique.The spectral hump has a shoulder structure as a rem-nant of the surface band. The lower surface band is deter-mined by tracing their energies, obtained as the crossingpoint of two lines fitted to a spectrum, as demonstrated in-0.100.90.80.70.30.20.10.80.60.40.20-0.2-0.2-0.100.90.80.7-0.2-0.10-101-101-10110Intensity (arb. unit)-0.1 0 0.1|SY|E − EF (eV)E − EF (eV)E − EF (eV)(a)(b)(c) (d)(e)SS1SS2Int.Int.MomentumE − EF (eV)kx (Å-1)kx (Å-1)kx (Å-1)|SY|Int.|SY||SY|~50 meVFIG. 3. Spin texture of surface states in Bi revealed by pump-probe spin-ARPES. (a,b) Spin polarization and spin-polarizedband along Γ − M, respectively. Red and blue represent up-and down-spin in the Y direction for two surface bands (SS1and SS2). The painted areas represent errors for plots in(a). (c) High-resolution map of spin polarization around Mwithin the black frame in (b). (d) Spin-resolved EDCs at k’smarked by arrows in (c). Energy positions of surface bandsare pointed by red and blue arrows. Black curves are theaddition of the up- and down-spin spectra. (e) Surface bandsdetermined from spin-resolved EDCs. Fitting curves to thedata (solid and dotted lines) are overlayed.Fig. 3(d). In Fig. 3(e), we plot the results together withthe upper surface band. In both bands, plots are missingclose to M, where the spin-polarization is zero; those are,instead, estimated by extrapolating a curve fitted to thedata (dotted curves). The upper surface band is almostflat, whereas the lower surface band disperses upward.However, they stay off each other, opening a band gap of∼50 meV at M. These observations eliminate the case ofFig. 1(g) predicted by most band calculations [14, 15].To pin down the relationship between the surface andbulk bands further, we measure high statistics data ofpump-probe ARPES around M [Fig. 4(a)]. The ob-tained intensity map [Fig. 4(a)] shows a parabola-shaped41.00.80.6-0.100.90.80.71.00.80.6-0.2-0.10(a)(c)(b)kx (Å-1)kx (Å-1) kx (Å-1)-0.103-0.087-0.071E − EF (eV)E − EF (eV) Intensity (arb. unit)E − EF  (eV)0.0490.0410.033-0.015-0.023-0.039-0.0550.008(d)ΔB < 20 meVΔS ~ 50 meVSS1SS20.02 eV0.22 eV< 0.35 eVEFFIG. 4. Bulk bands and their relationship with surface bands.(a) Pump-probe ARPES map around M. Here, the originalspectra are symmetrized across M to remove the matrix ele-ment effect. They are also divided by the Fermi-Dirac distri-bution function at the electron temperature (250 K) estimatedfrom the spectral edge broadening due to the pumping. (b)MDCs of (a). Thick black lines represent energies of two sur-face bands. Intensities of BCB and BVB are each paintedgreen and orange. (c) Bulk bands (color bars) obtained from(b) and surface bands (dashed lines) determined in Fig. 3(e)are superimposed. (d) Schematic band structure and charac-teristic energies obtained in our experiments.spectral continuum for the bulk valence and conductionbands (BVB and BCB), other than strong intensities forthe surface bands with spectral sharp peaks. To examinethe bulk states in more detail, we plot momentum dis-tribution curves (MDCs) around the bulk band gap inFig. 4(b), where the intensities for the bulk signals arepainted by colors (green and orange for BCB and BVB,respectively). Their intensities reduce the momentumwidth with approaching each other and eventually disap-pear without merging together. This indicates that a gap(< 0.02 eV) much smaller than that of the surface bands(∼ 0.05 eV) opens around E − EF = −0.025 eV. Thevalue of the bulk band gap we observed is consistent withthose (11 ∼ 15 meV) that have been determined by elec-tromagnetic experiments over the past half-century [43–47]. The bulk states are expressed in Fig. 4(c) withcolor bars. In the same panel, we overlay the upper andlower surface bands (dashed lines) determined from spin-polarized spectra in Fig. 3(e). The result shows that aTABLE I. Comparison of characteristic energies in bandstructures obtained: bottom of BCB at Γ, top of SS1 andSS2, and energy gap at M between BCB and BVB (∆B) andbetween SS1 and SS2 (∆S). Bulk topology is also listed.(eV) BCB (Γ) SS1 SS2 ∆B(M) ∆S(M) TopologyOur exp. < 0.35 0.22 0.02 < 0.02 ∼0.05 non-trivialOur calc. 0.21 0.18 0.04 0.06 0 trivialGGA [14] 0.29 0.26 0.06 0.1 0 trivialQSGW [15] 0.49 0.38 0.19 0.01 0 trivialsmall portion of the upper surface is absorbed into thebottom of BCB, whereas a large portion of the lowersurface band is into BCB around M, as depicted in Fig.4(d). The relation between surface and bulk bands corre-sponds to the case of Fig. 1(a). Hence, the bulk topologyof the elemental Bi is non-trivial (Z2=1; strong topo-logical insulator phase), against most theoretical predic-tions [14, 15] except for some exceptions [16].In previous studies, the comparison between data andcalculations on the bands of Bi has been limited to theoccupied states [17, 48]. In addition, a standard ARPESis out of reach for decisively distinguishing surface andbalk bands. These factors have prevented one from fairlyevaluating the reliability of band calculations for the el-emental Bi. Among modern experimental techniques, apump-probe spin-ARPES is the only means allowing afull comparison between the data and calculations, andit was first employed for Bi in this work.The characteristic values of bands obtained using thisunique experimental technique are described in Fig. 4(d):the bottom energy of BCB at Γ (see details in supplemen-tal materials), the top energies of two surface states (SS1and SS2), and the energy gaps between BCB and BVB(∆B) and between SS1 and SS2 (∆S) at M. These arecompared in Table 1 with the values of the generalizedgradient approximation (GGA) and quasi-particle self-consistent GW (QSGW) calculations [14, 15]. The GGAcalculations show good agreement with the data for thebottom of BCB and tops of the two surface bands; how-ever, ∆B(M) is over-estimated by ∼0.1 eV. In contrast,∆B(M) shows good agreement in the QSGW calcula-tions, in which, however, the energy position of BCB andtwo surface bands have large discrepancies of more than0.1 eV. We also conducted calculations with the Becke-Johnson (BJ) potential, as listed in Table 1. Again, amismatch with data by more than 0.1 eV is inevitable,and tuning parameters is necessary to obtain a non-trivialphase (see Supplemental Material).The debate on the bulk topology of Bi depends ona slight difference of band position in the energy scalemerely of several tens of meV. Considering that, the dis-crepancy as large as ∼0.1 eV from experiments revealedhere is quite serious for calculations [16]. In particu-5lar, the unoccupied states unveiled in this work moreclearly reveal discrepancies among calculations, provid-ing a strong restriction for evaluating the reliability of thecalculations. Our experimental results not only challengemodern band calculations but also provide good guide-lines for the future development of calculational methodsto agree with the present experiments eventually.In conclusion, we revealed the topological nature of theelemental Bi by solving the previous difficulties. Theseexperiments consistently reached the conclusion that Biis in the strong topological insulator phase (Z2=1). Ob-servation of the topological surface states further unveiledfascinating features with the spin-polarized saddle pointsgenerating van Hove singularity in the unoccupied den-sity of states. These topological surface bands form aspin helical structure at ∼0.2 eV, allowing one to controlmassive spin current by direct excitation with circularlypolarized mid-infrared light. 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