# Fileset

[Nakamura_et_al-2024-Communications_Materials.pdf](https://mdr.nims.go.jp/filesets/5f122a73-ccff-4ebd-ba80-deb88176a1fe/download)

## Creator

Tomonori Nakamura, Yitao Chen, Ryohei Nemoto, [Wenxuan Qian](https://orcid.org/0009-0003-2984-3108), Yuto Fukushima, Kaishu Kawaguchi, Ryo Mori, Takeshi Kondo, [Youhei Yamaji](https://orcid.org/0000-0002-4055-8792), [Shunsuke Tsuda](https://orcid.org/0000-0001-6209-8048), [Koichiro Yaji](https://orcid.org/0000-0002-0721-1316), [Takashi Uchihashi](https://orcid.org/0000-0003-0811-5665)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Moiré superlattices of antimonene on a Bi(111) substrate with van Hove singularity and Rashba-type spin polarization](https://mdr.nims.go.jp/datasets/3e7e4c26-a6a8-48c2-9cf2-eb4adf52a4e1)

## Fulltext

Moiré superlattices of antimonene on a Bi(111) substrate with van Hove singularity and Rashba-type spin polarizationcommunicationsmaterials Articlehttps://doi.org/10.1038/s43246-024-00615-zMoiré superlattices of antimonene on aBi(111)substratewithvanHovesingularityand Rashba-type spin polarizationCheck for updatesTomonori Nakamura1,2, Yitao Chen1,3, Ryohei Nemoto1, Wenxuan Qian1,3, Yuto Fukushima4,Kaishu Kawaguchi4, Ryo Mori4, Takeshi Kondo 4,5, Youhei Yamaji 1, Shunsuke Tsuda 6,Koichiro Yaji 6 & Takashi Uchihashi 1,3Moiré superlattices consisting of two-dimensional materials have attracted immense attentionbecause of emergent phenomena such as flat band-induced Mott insulating states andunconventional superconductivity.However, theeffects of spin-orbit couplingon thesematerials havenot yet been fully explored. Here, we show that single- and double-bilayer antimony honeycomblattices, referred to as antimonene, form moiré superlattices on a Bi(111) substrate due to latticemismatch. Scanning tunnelling microscopy (STM) measurements reveal the presence of spectralpeaks near the Fermi level, which are spatially modulated with the moiré period. Angle-resolvedphotoemission spectroscopy (ARPES) combinedwith density functional theory calculations clarify thesurface band structure with saddle points near the Fermi level, which allows us to attribute theobserved STM spectral peaks to the van Hove singularity. Moreover, spin-resolved ARPESmeasurements reveal that the observed surface states are Rashba-type spin-polarized. The presentwork has significant implications in that Fermi surface instability and symmetry breaking may emergeat low temperatures, where the spin degree of freedom and electron correlation also playimportant roles.The advent of artificially stacked two-dimensional (2D) materials withmoiré superlattices, which are induced by a lattice mismatch and/or a twistangle, has led to the development of new paradigms in condensed matterphysics and materials science1–3. The successful fabrication of graphene/hexagonal boronnitrideheterostructures and,more recently, twisteddoublelayers of graphene have spawned a series of exciting discoveries, e.g., Hof-stadter’s butterfly and fractal quantum Hall effect4–6, correlated insulatingstates and unconventional superconductivity7–9, charge order10, ferro-magnetismand thequantumanomalousHall effect11–14. The introductionofspin-orbit coupling (SOC) into moiré superlattices can lead to even richeremergent phenomena such as topological superconductivity, but thesestudies have been limited to transition metal dichalcogenides thus far14–18.The application of elemental 2D materials with strong SOCs may greatlyexpand the potential of moiré superlattices, but the exploration of such apossibility has been scarce thus far19.Bi and Sb are heavy VA elements with strong atomistic SOC andhence important ingredients in topological materials. The most stableform of bulk crystals is the A7 rhombohedral crystal structure, whichconsists of covalently bonded buckled honeycomb 2D layers (con-ventionally called bilayers) stacked by weak interlayer bonding20–22. Thisfeature makes Bi and Sb atomic layers promising 2D materials beyondgraphene23–25. Theywere theoretically predicted to become 2D topologicalinsulators (quantum spin Hall insulators), and their topological edgestateswere found experimentally26–32. They are also reported to be resilientagainst air exposure and chemical processes and thus can potentially beused for various practical applications23,24,33,34. Atomic layers of Bi and Sbare commonly referred to as bismuthene24,31 and antimonene23,25,34–40,while this nomenclature is not completely correct because they arebuckled and do not includes double bonds in their lattices23. Bismutheneand antimonene can be formed on an adequate substrate by molecular1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1, Namiki, Tsukuba, Ibaraki, Japan. 2Okinawa Institute ofScience and Technology Graduate University, 1919-1 Tancha, Onna-son, Kunigami-gun, Okinawa, Japan. 3Graduate School of Science, Hokkaido University,Kita-10 Nishi-8, Kita-ku, Sapporo, Japan. 4Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba, Japan. 5Trans-scale Quantum ScienceInstitute, The University of Tokyo, Bunkyo-ku, Tokyo, Japan. 6Center for Basic Research on Materials (CBRM), National Institute for Materials Science, 3-13,Sakura, Ibaraki, Japan. e-mail: UCHIHASHI.Takashi@nims.go.jpCommunications Materials |           (2024) 5:167 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00615-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00615-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00615-z&domain=pdfhttp://orcid.org/0000-0002-3912-5172http://orcid.org/0000-0002-3912-5172http://orcid.org/0000-0002-3912-5172http://orcid.org/0000-0002-3912-5172http://orcid.org/0000-0002-3912-5172http://orcid.org/0000-0002-4055-8792http://orcid.org/0000-0002-4055-8792http://orcid.org/0000-0002-4055-8792http://orcid.org/0000-0002-4055-8792http://orcid.org/0000-0002-4055-8792http://orcid.org/0000-0001-6209-8048http://orcid.org/0000-0001-6209-8048http://orcid.org/0000-0001-6209-8048http://orcid.org/0000-0001-6209-8048http://orcid.org/0000-0001-6209-8048http://orcid.org/0000-0002-0721-1316http://orcid.org/0000-0002-0721-1316http://orcid.org/0000-0002-0721-1316http://orcid.org/0000-0002-0721-1316http://orcid.org/0000-0002-0721-1316http://orcid.org/0000-0003-0811-5665http://orcid.org/0000-0003-0811-5665http://orcid.org/0000-0003-0811-5665http://orcid.org/0000-0003-0811-5665http://orcid.org/0000-0003-0811-5665mailto:UCHIHASHI.Takashi@nims.go.jpwww.nature.com/commsmatbeamepitaxy (MBE)31,34–37, in some cases leading to black phosphorus-likepuckered layers40,41.Here, we show by scanning tunneling microscopy (STM) that single-and double-bilayer (BL) antimonene formmoiré superlattices on a Bi(111)substrate due to lattice mismatch. They exhibit clear spectral peaks locatednear the Fermi level, which show distinctive behaviors regarding the moiréperiodicity. While the peaks found for single-BL antimonene show onlyweak modulations in height, those for double-BL antimonene are split by~100mV and exhibit strong spatial modulations, suggesting localizationdue to the moiré superlattice. Angle-resolved photoemission spectroscopy(ARPES) and spin-resolved ARPES (SARPES) combined with densityfunctional theory (DFT) calculations clarify the presence of saddle pointsnear the Fermi level. This allows us to identify the origin of the STMspectralpeaks as the van Hove singularity. These surface states are found to beRashba-type spin polarized. The present work has significant implicationsfor demonstrating that Fermi surface instability and symmetry breakingmay emerge at low temperatures, where the spin degree of freedom andelectron correlation are intimately involved.ResultsAtomic structures: STMmeasurementsAll the experiments were carried out in ultrahigh vacuum (UHV) chamberswith a base pressure of ~1×10−10 mbar (see Methods). First, a Bi(111) thinfilm was grown on a clean Si(111) surface to 10 BLs by MBE41,42. For theARPES/SARPES experimentswith an imaging-type instrument (see below),Ge(111) substrates were used because of easiness of sample preparation. Inthis case, a 250 BL-thick Bi(111) film was grown on a clean Ge(111)surface43,44. These two recipes resulted in essentially the sameBi(111) surfacestructures and did not affect our conclusion. Here, we adopt the rhombo-hedral crystallographic notation to describe the plane index of the film20,21.The crystallinity of the prepared samples was confirmed with scanningtunneling microscopy (STM) and low-energy electron diffraction (LEED).The surface of the Bi(111) film was then covered by 1–2 BL Sb (for LEEDpatterns, see Supplementary Information A). Since Bi(111) and Sb(111)bilayers share the same buckled honeycomb structure with similar latticeconstants of 0.454 nmand0.431 nm, respectively, a Sb(111)film could growepitaxially on a Bi(111) film45,46. However, the lattice constant of the free-standing Sb bilayer (1BL antimonene), which is predicted to be0.408–0.412 nm47,48, is significantly smaller than that of bulk Bi(111). Thisallows antimonene to grow nonepitaxially on Bi(111) and to form a moirésuperlattice, which we indeed observe as follows.The main panel of Fig. 1a shows a representative STM image of aBi(111) surface covered withmore than 1 BL of Sb. The lower terrace in theimage (Region I) features a triangular lattice structure, which is a moirésuperlattice made of 1BL antimonene (1BL Sb) on a Bi(111) surface.Although this superlattice includes defects and local deformations, thepresence of a well-defined periodicity is clear from its fast Fourier transform(FFT) image (inset of Fig. 1a). From repeated experiments with differentsurface regions and samples, we determined themoiré lattice constant to be4.70 ± 0.30 nm (Supplementary Information B). On the upper terrace, thereexists another region of the moiré superlattice with a longer periodicity(Region II). Since the height difference of ~0.4 nm between Regions I and II(Fig. 1b) is approximately equal to the height of the Sb bilayer (0.374 nm forbulk)20, Region II is identified as 2BL antimonene (2BL Sb) on a Bi(111)surface. Its moiré lattice constant was determined to be 6.59 ± 0.89 nm. Therelatively large uncertainty is due to variations throughout different surfaceregions, presumably reflecting very small differences in energy. This 2BL Sblayer is borderedby another1BLSb layer (Region III),which is located in theupper-right corner of the image. Since they have almost the same topo-graphic heights20, the boundary (indicated by the dashed line) is identified asthe location of a buried atomic step of the Bi(111) surface. Our repeatedexperiments indicate that antimonene layers grow from the step edges ofBi(111) surfaces.They also show that 2BLSb layers begin to growbefore 1BLSb layers fully cover thewhole surface, but 1BL Sb layers occupy~70%of thetotal area when the nominal coverage θ of Sb is 1.0 BL. The same trend alsoapplies to the growth of 2BL Sb. Therefore, 1BL and 2BL Sb are the domi-nant phases for θ = 1.0 BL and 2.0 BL, respectively (SupplementaryInformation C).Magnified STM images of 1BL and 2BL Sb are displayed in Figs. 1c, d,respectively, where the Sb atomic lattices are clearly resolved. Themoiré unita c deABAC AA2 nmACABAA2 nmAA AB ACIIIIII20 nm0.60.40.20.0806040200height (nm)distance (nm)bFig. 1 | Topographies and atomic structures of antimonene/Bi(111) moirésuperlattices. a STM topographic image of 1BL and 2BL Sb grown on a Bi(111) film(Sample bias voltage: Vs =−1.0 V, Tunnelling current: It = 100 pA). Regions I andIII correspond to 1BL Sb while Region II to 2BL Sb. The inset shows a FFT transformof a surface area belonging to Region I (scale bar: 0.3 nm−1). b Height profile alongthe dotted line in a. c, d Atomic resolution images of 1BL Sb c and 2BL Sb d on aBi(111) surface. (Vs =−50 mV, It = 500 pA c, Vs =−50 mV, It = 300 pA d). Thedashed parallelograms indicate the unit cells of themoiré superlattices. eThe top andside views of the AA, AB and AC stacking sequences (blue spheres: Sb, red spheres:Bi). The vertical dashed lines shows the alignment of the Sb and Bi atoms.https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 2www.nature.com/commsmatcells are indicated by the dashed parallelograms. These features are ascribedto the surface topography because they are reproduced with different biasvoltages (for example, see Fig. 2a, d below). We determined the latticeconstant of 1BL Sb to be 0.415 ± 0.004 nm (Supplementary Information B).The fact that this value is greater than that of free antimonene(0.408–0.412 nm)47,48 is attributed to the tensile strain exerted from theBi(111) surface. Likewise, the lattice constant of 2BL Sb was determined tobe 0.423 ± 0.005 nm. This value is closer to that of bulk Sb(111) (0.431 nm)than that of 1BL Sb, suggesting lattice relaxation toward the bulk crystal.Combined with the moiré lattice constant determined above, the numbersof Bi and Sb atoms included in the moiré superlattice can be calculated.Assuming that the moiré unit cell consists of NBi ×NBi Bi atoms andNSb ×NSb Sb atoms per layer (NSb =NBi+ 1), we findNBi = 10,NSb = 11 for1BL Sb andNBi = 13–17,NSb = 14–18 for 2BL Sb. Our FFT analysis of STMimages over an extended area reveals that there is no twisting between themoiré and Sb lattices on average (Supplementary Information B), althoughthere are some local deviations due to deformations. Furthermore, Fig. 1c, dshows that the surface is divided into three characteristic regions in terms oftopographic height. By comparing these observations to previous reports onrelatedmoiré superstructures49–53, we can safely assign them to the regions ofthe AA, AB, and AC stacking sequences (Fig. 1e). In the AA stacking, allatoms in the two layers are vertically overlapped, while only half of them arein the AB and AC stacking layers. Because of the significant buckling of thehoneycomb lattice, the vertical distance between the overlapping atoms inthe AB stacking is greater than that in the AA stacking. This leads to thelowering of the top layer by an attractive force. Conversely, in the ACstacking, the vertical distance between the overlapped atoms is smaller thanthat in the AA stacking. This leads to the raising of the top layer by arepulsive force. As a result of structural relaxation, the areas correspondingto the AB and AC stacking regions expand and shrink, respectively49,50.These features are clearly observed in Fig. 1c, d.Electronic structures: STS measurementsThe electronic states of the moiré superlattices and their spatial modulationswere investigated by scanning tunnelling spectroscopy (STS). First, for 1BLSb on Bi(111), dI/dV spectra were taken at the center of the AA stackingregion at five locations, and this process was repeated for the AB and ACstackings. The selected spectral sites are shown in the topographic STMimage in Fig. 2a with red (AA), blue (AB), and green (AC) squares. Figure 2bshows the results of the STS measurements. The broken lines show indivi-dual dI/dV spectra, and the solid lines show the average values for the samestacking sequences, with their colors corresponding to those in Fig. 2a. Theaverage of all the measured spectra are also shown by the solid black line. Forall of these spectra, clear peak structures are noticeable near the zero bias302520151050-200 0 200 average AA AB AC302520151050-200 0 200Vbias (mV) average AA AB ACa b cd e5 nm5 nmfABAAACACACABAAACAA AB ACAA AB ACV (mV)dI/dV(arb. unit)V (mV)dI/dV(arb. unit)V (mV)V (mV)height (nm)height (nm)distance (nm)distance (nm)Fig. 2 | Local electronic structures of antimonene/Bi(111) moiré superlatticesnear the Fermi level. a STM topographic image of 1BL Sb/Bi(111) moiré super-lattices (Vs = -300 mV, It = 100 pA). The red (AA), blue (AB), and green (AC)squares show the locations for the STS measurements. b dI/dV spectra obtained atindividual locations shown in a (broken lines) and their averages (solid lines) takenfor the same stacking sequences. The red, blue, and green lines correspond to AA,AB, and AC stackings, respectively. The black solid line is the average of all thespectra. c (Right panel) 2D plot of color-coded dI/dV spectra of 1BL Sb/Bi(111)moiré superlattices, which was taken along a straight line connecting the centers ofAC, AB, AA, and AC regions (Vs = -300 mV, It = 100 pA). The vertical axis repre-sents the lateral distance from the starting point. (Left panel) Topographic crosssection along the measurement line. d–f Results for 2BL Sb/Bi(111) moiré super-lattices obtained in the samemannerwith the identical imaging parameters as in a–c.https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 3www.nature.com/commsmatvoltage, with the full width at half maximum of 80− 100mV. The spectralpeaks at the AB sites are particularly conspicuous, while those at the AA andAC sites are relatively suppressed. More detailed information was obtainedthrough line spectroscopy; dI/dV spectra were taken along a straight lineconnecting the centers of the AC, AB, AA, andAC sites in this sequence. Theright panel of Fig. 2c shows a 2D plot of color-coded dI/dV spectra as afunction of bias voltage and lateral distance from the starting point. In the leftpanel of Fig. 2c, the topographic profile along the line is also shown.We findthat the spectral peak is fixed at approximately 0− 30mV, while its intensityvaries. This result strongly suggests the presence of delocalized states aroundthe Fermi level that are weakly modulated by the moiré superlattice.Figure 2d–f displays site-dependent dI/dV spectra for 2BL Sb onBi(111) obtained in the same manner. The symbols and colors used in thefigure follow the conventions of Fig. 2a–c. Figure 2e shows that spectralpeaks are shifted from zero bias by 48mV (AA site), -48mV (AB site), and144mV(ACsite) on average. The right panel of Fig. 2f shows that clear peakstructures at approximately 40mV and -100mV are confined within theAA and AB regions, respectively. This result indicates the presence ofmultiple states near the Fermi level that are localized due to the moirésuperlattice54.Electronic structures: ARPES/ SARPES measurementsTo clarify the origin of the spectral peaks observed by STS, we performedlaser-based high-resolution ARPES/SARPES measurements55. Forsimplicity, the data were analyzed based on the Brillouin zone of Bi(111)(Fig. 3a). First, we focused on the results for 1BL of Sb on a Bi(111) surface.Figure 3b shows a 2Dplot of theARPES intensity along the�Γ� �Mdirectionand as a binding energy EB (dark: high, bright: low). We can recognize twobands, denoted as S1 and S2, starting from an EB≅ 0.2 eV and dispersingupward. These bands disappear at approximately kx = 0.05–0.1 Å−1 bycrossing the Fermi level but seem to disperse downward and reappear atapproximately kx = 0.4–0.5 Å−1. The band dispersions determined from theplot are highlightedwith red dashed curves. The signals are better visualizedby the SARPES signal plotted for the range of -0.22 Å−1 < kx <+0.22 Å−1,where the intensity and the spin polarization in the y direction are indicatedby brightness (dark: high, bright: low) and color (red: positive, blue: nega-tive), respectively. The maximum spin polarization of the photoelectron is~0.6. The spin polarizations of the S1 andS2 bands are opposite to eachotherand are antisymmetric with respect to kx = 0 Å−1. This is characteristic ofRashba-type spin-polarization, which will be discussed later. Figure 3cshows a similar 2D plot of the ARPES intensity along the �Γ� �K (ky)direction. The S1 and S2 bands are also noticeable (highlighted with reddashed lines), but the S2 band reaches a localmaximumnear the Fermi levelat approximatelyky = 0.1- 0.15 Å−1 and thendisperses downward. Forbettervisibility, the same ARPES data in Fig. 3b, c are displayed in Fig. D2a, bwithout red dashed lines (Supplementary Information D).Figure 3e shows the 2D plot of the ARPES intensitymeasured near theFemi level (EB = 0.02 eV) in the kx–ky space, which gives the Fermi surfaceFig. 3 | Electronic and spin structures of 1BL antimonene/Bi(111) moirésuperlattices in the momentum space. a Bi(111) Brillouin zone and the highsymmetry points �Γ; �M; �K; �K0 . The green rectangle and the red square correspond tothe areas for e and f, g, respectively. b 2D plot of ARPES intensity as a function ofmomentum kx along the �Γ� �Mdirection and as a binding energyEB. cThe same plotas inb along the �Γ� �Kdirection. The orange and blue rectangles correspond to thoseshown in Fig. 4a.d 2Dplot of the SARPES signal as a function ofmomentum kx alongthe �Γ� �M direction and as a binding energy EB. The intensity and the spin polar-ization in the y direction are indicated by brightness (dark: high, bright: low) andcolor (red: positive, blue: negative), respectively. In b–d, the dispersions of S1 and S2bands are indicated by the red dashed lines. e 2D plot of ARPES intensity measurednear the Femi level (EB = 0.02 eV) in the kx–ky space, which gives the Fermi surfacecontour. The plot includes two data sets obtained in separate runs, which causes anapparent discontinuity at kx = 0.12 Å-1. The dashed lines indicate the �Γ� �K direc-tions. The red ellipses show the locations of the saddle points of the S2 band. f Thesame plot as in e in a largermomentum space, which was obtained with the imaging-type instrument. g 2D plot of SARPES intensity and spin polarization in the ydirection measured near the Fermi level (EB = 0.03 eV) obtained with the imaging-type instrument. The intensity and the spin polarization in the y direction are plottedas in d. The Fermi surface contour of the S2 band determined from f is shown withred solid lines. The black and white dashed lines indicate the �Γ� �M directions.https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 4www.nature.com/commsmatcontour. The central ring and a surrounding star-like structure are clearlynoticeable and canbe identified as theS1 andS2 bands, respectively.Notably,some parts of the S2 band appear very weak due to the anisotropic transferduring the photoemission process. By referring to the band dispersions inFig. 3b-d, we can identify the areas indicated by the red ellipses as saddlepoints, where the S2 band takes a local maximum in the �Γ� �K direction(k = 0.1–0.15 Å−1, EB ~ 0 eV; see Fig. 3c) and a local minimum in theorthogonal direction. This means that the vanHove singularity exists at theFermi level56 and explains the origin of the zero bias peak for 1BL Sb/Bi(111)described above. To confirm this result, we also performed Fermi surfacemapping with an imaging-type ARPES instrument, which allows us toaccess a larger momentum space at a faster speed (Fig. 3f)44. The acquiredFemi surface well reproduces the features observed in Fig. 3e while betterreflecting the sixfold symmetry expected from the C3 and time-reversalsymmetries of the present system. We note that the band structure and theFermi surface resemble those of Bi(111) andSb(111) surfaces21,42,43,57,58, whilesaddle points are absent near the Fermi level in the latter cases.Because of the space-inversion symmetry breaking at surface andstrong SOC of Sb and Bi, Rashba-type spin polarization is expected. Toconfirm this, the distribution of spin polarization in momentum space wasinvestigated with the same imaging-type instrument for 1BL Sb/Bi(111).Figure 3g shows a 2D plot of the SARPES intensity and spin polarization inthe y direction (Py) measured near the Fermi level (EB = 0.03 eV). Theobserved signal is mostly attributed to the S2 band, the location of which isreproduced from Fig. 3f (red solid lines). Along the kx axis (white dashedline) andnear the�Γ� �K lines at ± 60° to the kx axis (blackdashed lines),Py isreversed when momentum is reversed with respect to the �Γ point (see alsoSupplementary Information D, Fig. D3), although their intensities are dif-ferent. The variations in the intensity can be attributed to the fact thatSARPES (more generally, ARPES) signal is strongly dependent on thetransitionmatrix in the photoemission process. These results are consistentwith Rashba-type spin polarization. We should note that the actual dis-tribution of spin polarization deviates from the ideal vortical form, asindicated by the reversal of Py with respect to the black dashed lines. Ananalogous behavior was also predicted and observed for a clean Bi(111)surface with a giant Rashba splitting44,59,60.We also performed ARPES/SARPES measurements of 2BL Sb on aBi(111) surface (Supplementary Information D, Fig. D1). These results arenearly identical to those for 1BLSb/Bi(111) (Fig. 3), but the observedARPESsignals are clearer than those for 1BL Sb/Bi(111). This difference may beattributed to the better moiré periodicity observed with STM (Fig. 1a).Electronic structures: DFT calculationsAb initio calculations of the electronic structure of Sb/Bi(111) moirésuperlattices are difficult because of the large number of heavy atomsinvolved within a moiré unit cell. To circumvent this problem, we carriedout DFT calculations based on an epitaxial model consisting of 1BLSb(111) on 5BL Bi(111) (Methods). Although thismodel does not includethe effect of moiré periodicity, it can account for the overall band struc-tures within the Bi(111) Brillouin zone. The structural relaxation withineach stacking region in the actual moiré structure (Fig. 1c, d) rationalizesthis treatment. Figure 4b shows the band diagram calculated for the epi-taxialmodelwith theAB stacking (Fig. 4a). The orange andblue rectanglescorrespond to the same marked areas in Fig. 3b,c. The sizes of the purple(light blue) circles represent the contributions of the top Sb (Bi) BL.Overall, the two bands starting from the �Γ point below the Fermi level(designated by the reddashed lines) aremostlyderived from the topSbBL,indicating that they can be preferentially detected in surface-sensitiveSTMandARPESmeasurements. Judging from their dispersions, they canbe assigned to the S1 and S2 bands identified above (Fig. 3b-d). Otherbands with negligible contribution of Sb are assigned to the Bi(111) sur-face states on the back side of the model and thus are irrelevant to ourexperimental data. The same calculations for the AA and AC stackingsgive very similar band structures near the �Γ point and around the Fermilevel (Supplementary Information E, Fig. E2b and Fig. E3b). Therefore,the presence of saddle points near the Fermi level is theoretically con-firmed. The energies E-EF and momenta (kx, ky) of the saddle points aresummarized in Table E1 of Supplementary Information E. These featuresare reflected in the projected density of states (PDOS) on the top Sb BL(Fig. 4g). The three sharp peaks indicated by the arrows at E – EF = 0.02 –0.05 eV, corresponding to theAA,ABandACstackings, are due to the vanHove singularity of the saddle point. The peak energies are very close toone another, reproducing the STS results shown in Fig. 2b,c. Assumingthat the Fermi level is aligned near these peaks in real samples, we plot theFermi surface contour of 1BL Sb(111)/5BLBi(111)withAB stacking atE –EF = -0.02 eV (Fig. 4c). The central rings and a surrounding star-likestructure are consistent with the ARPES results (Fig. 3e, f). The spinstructures at the Fermi surface calculated for this model is consistent withthe SARPES plot in Fig. 3g (Supplementary Information E, Fig. E4).The same calculations were also conducted based on an epitaxialmodel of 2BL Sb(111) on 5BL Bi(111) (Fig. 4d). The band structuresand the Fermi surface (E – EF = -0.02 eV) obtained for the AB stack(Fig. 4e, f) resemble those obtained for the 1BL Sb(111) model(Fig. 4b, c) as well as the ARPES results (Supplementary Informa-tion D, Fig. D1). This is also the case for the AA and AC stackings(Supplementary Information E, Fig. E2d–f and Fig. E3d–f). However,the PDOSs around the Fermi level calculated for the AA, AB, and ACstacks exhibit more separated energies (Fig. 4h). Qualitatively, theseresults are in line with the STS data (Fig. 2e, f), but there are someclear discrepancies; e.g., the sharp peak at E – EF = 0 eV for the ACstacking has no corresponding structure in the STS data (Fig. 2e).This difference may be attributed to incomplete structural optimi-zation of the 2BL Sb model, which results from our simplified modelsof fixing the locations of the Bi atom to those of the bulk Bi crystal(see Methods).DiscussionWecalculated the band structures of antimonene on aBi(111) surface basedon epitaxial models of 1BL Sb(111)/5BL Bi(111) and 2BL Sb(111)/5BLBi(111), which successfully explained our STMandARPESdata.Obviously,the adoptedmodels are rather crude and do not include the effects of moirémodulations. The fact that all stacking sequencies AA, AB, andAC result inqualitatively identical electronic band structures may also explain the suc-cess of the present models. Experimentally, the 1BL-Sb/Bi(111) moirésuperlattice has nearly no spectral modulation (Fig. 2c), while the 2BL-Sb/Bi(111) moiré superlattice has a modulation of 0.1− 0.2 eV (Fig. 2f).Considering that the transfer integrals between the atomic orbitals inneighboring layers of Bi and Sb are 0.3 − 1.4 eV20, the influences of moirésuperlattices are unexpectedly small. It suggests that it is not simply deter-mined by the interlayer coupling strength.Since Sb and Bi are isovalent, replacing Bi by Sb at the top layer simplyleads to variations in electrostatic potential. It is thus possible to interpret thepresent S2band, featuring the saddlepointsnear theFermi level, as a result ofcontinuous deformation of the S2 band of a clean Bi(111) surface61.We alsonote that Bi is a topologically nontrivial semimetal and that its (111) surfacestates are protected43,62. Based on the same ground, the surface states ofantimonene on Bi(111) can be topologically equivalent to those on Bi(111).In this case, the formation of an energy gap within the surface states isprohibited because it would violate the requirement that the bulk conduc-tion and valence bands be continuously connected by surface states63,64.Indeed, our DFT calculations based on a moiré superlattice model indicatethat there are no moiré-induced energy gaps at the zone boundary (seeSupplementary Information F, Fig. F1). The result may be attributed to thetopological protection discussed above. In this case, (high-order) van Hovesingularities are predicted to emerge at the �K point of the moiré Brillouinzone63, which calls for a future study.Here we brieflymention the possibility of alloying of the top layer. It iswidely known that Sb and Bi can form alloys with arbitrary ratios, and thusSb and Bi atoms may be mixed to some extent. However, since the alloyformation does not change the A7 rhombohedral crystal structure of bulk65,https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 5www.nature.com/commsmatit is highly likely to retain the buckled honeycomb lattice of antimonene.Since Sb and Bi are isovalent, the main effect of the mixing should be asimple potential modulation, which may slightly shift the band energy.Nevertheless, considering the good agreement between the band structureobtained byARPES and that of our theoreticalmodel, the alloying effect canbe neglected for the current data set.Finally, we discuss the implications of the findings in the present work.Generally, the presence of the van Hove singularity means a logarithmicdivergence of the density of states and an enhancement of Coulombinteractions. Tuning the Fermi level to a vanHove singularity point can leadto a variety of symmetry-broken phases at low temperatures, such asunconventional superconductivity, charge density waves, ferromagnetism,charge order, and nematicity; these phases have been discussed within thecontext of high-Tc cuprates, graphene, kagome metals, etc56,66–69. Since thevan Hove singularities in our systems are located close to the Fermi level,their tuning must be technically viable through gate voltage or moleculardoping70. Among the possible low-temperature phases, superconductivity isthemost likely because of the presence of Rashba-type spin polarization andthe resulting spin-momentum locking63. In this case, the absence of spaceinversion symmetry should lead to a spin singlet-triplet mixed state71. Wenote that electron‒phonon coupling, which is responsible for super-conductivity, is likely to be enhanced here, as discussed for granular Bifilms72,73. Regarding 2BL Sb/Bi(111), moiré-induced electron confinementand enhanced electron correlation can further enrich the low-temperaturephysics beyond the simple van Hove singularity scenario. The inclusion ofRashba-type spin polarization in themoiré system is an open and intriguingproblem. Experimentally, preparation of a high-quality sample with lessstructural defects and a better moiré periodicity would be essential, since itshould strengthen the divergent behavior of the vanHove singularity. Thus,the present Sb/Bi(111) moiré superlattices will offer a new playground forinvestigating the role of the spin degree of freedom in van der Waalsmaterials.Fig. 4 |DFTband structure calculations for the Sb(111)/Bi(111) epitaxialmodels.a, dAtomic structure models for 1BL Sb(111)/5BL Bi(111) (a) and 2BL Sb(111)/5BLBi(111) (d) with the AB stacking. The solid rectangles are the unit cells for calcu-lations. b, eBand dispersions along the �K� �Γ� �Mdirection calculated with the 1BLSb(111)/5BL Bi(111)model (b) and the 2BL Sb(111)/5BL Bi(111)model (e) with ABstacking. The orange and blue rectangles correspond to those shown in Figs. 3b and3c. The sizes of the purple (light blue) circles represent the contributions of the top Sb(Bi) BL. c, f Fermi surfaces (E – EF = -0.02 eV) calculated for the 1BL Sb(111)/5BLBi(111) model (c) and the 2BL Sb(111)/5BL Bi(111) model with AB stacking (f). Thecolors represent the Fermi velocity (red: fast, blue: slow). The red squares correspondto the regions displayed in Fig. 3f, g. g, h Projected density of states (PDOS) on thetop Sb BL calculated for the 1BL Sb(111)/5BL Bi(111) model (g) and the 2BLSb(111)/5BL Bi(111) model (h).https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 6www.nature.com/commsmatMethodsSample preparationThe Si(111) substrates were cleaned by direct current heating at 1250 °C for10 seconds. After repeating the cycle several times, 7× 7 clean surfaces wereobtained. The Ge(111) substrates were cleaned by repeated Ar+ sputteringand annealing several times to obtain 2 × 1 surfaces. Both surfaces wereconfirmed by observing sharp LEED spots. Bi(111) films were then grownbyMBE on Si(111)-7× 7 surfaces to 10 BLs or on Ge(111)-2 × 1 surfaces to250 BLs at room temperature. To improve the flatness of the film, the Bifilms were annealed at approximately 190 °C for 5min. Subsequently, Sbwas deposited on the Bi(111) surfaces at room temperature to form moiréantimonene. The crystallinity of the sample was improved by mildannealing at approximately 100 °C.STMmeasurementsThe STMmeasurements were conducted at 78 K and 4.6 K with a Nanoniscontroller Mimea BP5e. Topographic images were obtained in constantcurrent mode. The lateral scale of the STM images was calibrated throughobservation of Bi(111) surfaces by assuming that the lattice constant isequivalent to that of a bulk crystal (0.454 nm). STS measurements wereconducted with a built-in lock-in amplifier with a typical bias voltagemodulation of 20mV at 477 Hz.ARPES measurementsARPES and SARPES measurements were performed at National Institutefor Materials Science (NIMS) and at the Institute for Solid State Physics(ISSP), University of Tokyo. For the NIMS measurements, we employed amomentummicroscope equippedwith an imaging spindetector44,74.A10.9-eV laser was used as the excitation light. For the measurements at the ISSP,the photoelectrons excited by a 6.994-eV laser were analyzed by a hemi-spherical photoelectron analyzer equipped with an ultralow-speed electrondiffraction spin detector55. For both measurements, samples were preparedin situ. The sample temperature during the measurements was 30 K.DFT calculationsTo calculate the electronic band structures, we adopted epitaxialmodels of 1BL Sb(111)/5BL Bi(111) and 2BL Sb(111)/5BL Bi(111).The locations of the Bi atoms and those of the Sb atoms in the in-plane directions were fixed to those of the bulk Bi crystal. The out-of-plane Bi atom positions follow the structure for the Bi(111) thin filmused in the literature61. Here, the Bi atom locations in the top Bi BL(adjacent to the Sb BLs) are modified, while the other Bi atoms followthe bulk Bi structure. In contrast, the locations of the Sb atoms in theout-of-plane direction were set equal to those at the centers of theAA, AB and AC stacking regions of the numerically optimized moirésuperlattices (indicated by the red, blue and green circles, respec-tively, in Fig. E1; see Supplementary Information E). To optimize the1BL Sb(111)/5BL Bi(111), we prepared a single 11 × 11 supercell ofthe Sb(111) BL on five vertically stacked 10 × 10 supercells of theBi(111) BL. While the locations of the Bi atoms are fixed as in theBi(111) thin film61, the locations of the Sb atoms are optimized byutilizing a neural network potential, PFP (without U) version 5.0.0,on Matlantis (https://matlantis.com/)75. Similarly, to optimize the2BL Sb(111)/5BL Bi(111), we prepared two 14 × 14 supercells of theSb BL on five 13 × 13 supercells of the Bi BL and optimized thepositions of the Sb atoms.The noncollinear DFT calculations for the epitaxial models are per-formed by OpenMX version 3.976–79 with the PBE exchange correlationfunctional and spin–orbit coupling. We use the 15 × 15 × 1 k-point grid inthe first Brillouin zone for self-consistent field (SCF) calculations. After theSCF calculation, the density of states is obtained on a 256 × 256 × 1 k-pointgrid by the tetrahedron method. The energy cutoff is set to 100 or 200 Ry.The dependence of the band structure and density of states on the k-pointgrid and energy cutoff was examined to ensure convergence.Data availabilityThe datasets generated during and/or analyzed during the current study areavailable from the corresponding author upon reasonable request.Received: 19 April 2024; Accepted: 14 August 2024;References1. Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivityand strong correlations inmoiré flat bands.Nat. Phys. 16, 725–733 (2020).2. Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat.Mater. 19, 1265–1275 (2020).3. He, F. et al. Moiré patterns in 2D materials: a review. ACS Nano 15,5944–5958 (2021).4. Hunt, B. et al. MassiveDirac fermions andHofstadter butterfly in a vander Waals heterostructure. Science 340, 1427–1430 (2013).5. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Halleffect in moiré superlattices. Nature 497, 598–602 (2013).6. Cheng, B. et al. Fractional and symmetry-broken chern insulators intunable Moiré superlattices. Nano Lett. 19, 4321–4326 (2019).7. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80 (2018).8. Cao, Y. et al. Unconventional superconductivity in magic-anglegraphene superlattices. Nature 556, 43 (2018).9. Lu, X. et al. Superconductors, orbitalmagnets and correlated states inmagic-angle bilayer graphene. Nature 574, 653–657 (2019).10. Jiang, Y. et al. Chargeorder andbroken rotational symmetry inmagic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).11. Sharpe, A. L. et al. Emergent ferromagnetism near three-quartersfilling in twisted bilayer graphene. Science 365, 605–608 (2019).12. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiréheterostructure. Science 367, 900–903 (2020).13. Liu, X. et al. Tunable spin-polarized correlated states in twisteddoublebilayer graphene. Nature 583, 221–225 (2020).14. Chen,G. et al. TunablecorrelatedChern insulator and ferromagnetismin a moiré superlattice. Nature 579, 56–61 (2020).15. Wang, L. et al. Correlated electronic phases in twisted bilayertransition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).16. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2moiré superlattices. Nature 579, 353–358 (2020).17. Hennighausen, Z. et al. Evidence of a purely electronic two-dimensional lattice at the interface of TMD/Bi2Se3 heterostructures.Nanoscale 11, 15929–15938 (2019).18. Kezilebieke, S. et al. Moiré-Enabled Topological Superconductivity.Nano Lett. 22, 328–333 (2022).19. Le Ster, M., Maerkl, T., Kowalczyk, P. J. & Brown, S. A. Moir\‘epatterns in van der Waals heterostructures. Phys. Rev. B 99,075422 (2019).20. Liu, Y. & Allen, R. E. Electronic structure of the semimetals Bi and Sb.Phys. Rev. B 52, 1566–1577 (1995).21. Hofmann, P. The surfaces of bismuth: Structural and electronicproperties. Prog. Surf. Sci. 81, 191–245 (2006).22. Bian, G. et al. Survey of electronic structure of Bi and Sb thin films byfirst-principles calculations and photoemission measurements. J.Phys. Chem. Solids 128, 109–117 (2019).23. Ares, P., Palacios, J. J., Abellán, G., Gómez-Herrero, J. & Zamora, F.Recent Progress on Antimonene: A NewBidimensionalMaterial.Adv.Mater. 30, 1703771 (2018).24. Liu, X. et al. Advances of 2D bismuth in energy sciences.Chem. Soc.Rev. 49, 263–285 (2020).25. Xue,C.-L. &Li, S.-C.Recentprogressonantimonene: from theoreticalcalculation to epitaxial growth. Jpn. J. Appl. Phys. 60, SE0805 (2021).26. Murakami, S. Quantum Spin Hall Effect and Enhanced MagneticResponsebySpin-Orbit Coupling.Phys. Rev. Lett. 97, 236805 (2006).https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 7https://matlantis.com/www.nature.com/commsmat27. Zhang,P., Liu, Z., Duan,W., Liu, F. &Wu, J. Topological and electronictransitions in a Sb(111) nanofilm: The interplay between quantumconfinement and surface effect. Phys. Rev. B 85, 201410 (2012).28. Chuang, F.-C. et al. Tunable topological electronic structures inSb(111) bilayers: A first-principles study. Appl. Phys. Lett. 102,022424 (2013).29. Drozdov, I. K. et al. One-dimensional topological edge states ofbismuth bilayers. Nat. Phys. 10, 664–669 (2014).30. Kim, S. H. et al. Topological phase transition and quantum spin Halledge states of antimony few layers. Sci. Rep. 6, 33193 (2016).31. Reis, F. et al. Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material. Science 357, 287–290 (2017).32. Peng, L. et al. Visualizing topological edge states of single and doublebilayer Bi supported on multibilayer Bi(111) films. Phys. Rev. B 98,245108 (2018).33. Ares, P. et al. Mechanical Isolation of Highly Stable Antimonene underAmbient Conditions. Adv. Mater. 28, 6332–6336 (2016).34. Wu, X. et al. Epitaxial Growth and Air-Stability of MonolayerAntimonene on PdTe2. Adv. Mater. 29, 1605407 (2017).35. Shao, Y. et al. Epitaxial Growth of Flat AntimoneneMonolayer: A NewHoneycombAnalogueofGraphene.NanoLett.18, 2133–2139 (2018).36. Fortin-Deschênes, M. et al. Synthesis of Antimonene on Germanium.Nano Lett. 17, 4970–4975 (2017).37. Ji, J. et al. Two-dimensional antimonene single crystals grown by vander Waals epitaxy. Nat. Commun. 7, 13352 (2016).38. Zhang,S., Yan,Z., Li, Y., Chen,Z. &Zeng,H.Atomically ThinArseneneand Antimonene: Semimetal–Semiconductor and Indirect–DirectBand-Gap Transitions. Angew. Chem. Int. 54, 3112–3115 (2015).39. Aktürk,O. Ü., Özçelik, V. O. &Ciraci, S. Single-layer crystalline phasesof antimony: Antimonenes. Phys. Rev. B 91, 235446 (2015).40. Zhang,P. et al. Absence of topologicalβ-antimoneneandgrowthofα-antimonene on noble metal Ag(111) and Cu(111) surfaces. Phys. Rev.Mater. 6, 074002 (2022).41. Nagao, T. et al. Nanofilm Allotrope and Phase Transformation ofUltrathin Bi Film on Si(111)-7×7. Phys. Rev. Lett. 93, 105501 (2004).42. Hirahara, T. et al. Role of Spin-Orbit Coupling and HybridizationEffects in theElectronicStructureofUltrathinBi Films.Phys.Rev. Lett.97, 146803 (2006).43. Ito, S. et al. Proving Nontrivial Topology of Pure Bismuth by QuantumConfinement. Phys. Rev. Lett. 117, 236402 (2016).44. Yaji, K. & Tsuda, S. Visualization of spin-polarized electronic states byimaging-type spin resolved photoemissionmicroscopy.Sci. Technol.Adv. Mater. Meth. 4, 2328206 (2024).45. Takayama, A., Sato, T., Souma, S. & Takahashi, T. Rashba effect inantimony and bismuth studied by spin-resolved ARPES. N. J. Phys.16, 055004 (2014).46. Abe, H., Iwasawa, D., Imamura, M., Takahashi, K. & Takayama, A.Electronic structure of Sb ultrathin film on Bi(111) with large latticemismatch. AIP Adv. 13, 055303 (2023).47. Wang, G., Pandey, R. & Karna, S. P. Atomically Thin Group VElemental Films: Theoretical Investigations of AntimoneneAllotropes.ACS Appl. Mater. Interfaces 7, 11490–11496 (2015).48. Liu, G., Gao, Z. & Zhou, J. Strain effects on the mechanical propertiesof Group-V monolayers with buckled honeycomb structures. Phys. ELow. Dimens 112, 59–65 (2019).49. An, Q., Moutanabbir, O. & Guo, H. Moiré patterns of twisted bilayerantimonene and their structural and electronic transition. Nanoscale13, 13427–13436 (2021).50. Naik, M. H. & Jain, M. Ultraflatbands and Shear Solitons in MoiréPatterns of Twisted Bilayer Transition Metal Dichalcogenides. Phys.Rev. Lett. 121, 266401 (2018).51. Li, E. et al. Lattice reconstruction induced multiple ultra-flat bands intwisted bilayer WSe2. Nat. Commun. 12, 5601 (2021).52. Liu, B. et al.Moiré Pattern Formation in EpitaxialGrowthon aCovalentSubstrate: Sb on InSb(111)A. Nano Lett. 23, 3189–3195 (2023).53. Li, H. et al. Imaging moiré flat bands in three-dimensional reconstructedWSe2/WS2 superlattices. Nat. Mater. 20, 945–950 (2021).54. Pan, Y. et al. Quantum-Confined Electronic States Arising from theMoiré Pattern of MoS2–WSe2 Heterobilayers. Nano Lett. 18,1849–1855 (2018).55. Yaji, K. et al. High-resolution three-dimensional spin- and angle-resolved photoelectron spectrometer using vacuum ultraviolet laserlight. Rev. Sci. Instrum. 87, 053111 (2016).56. Markiewicz, R. S. A survey of the Van Hove scenario for high-tcsuperconductivity with special emphasis on pseudogaps and stripedphases. J. Phys. Chem. Solids 58, 1179–1310 (1997).57. Sugawara, K. et al. Fermi Surface and Anisotropic Spin-OrbitCoupling of Sb(111) Studied by Angle-Resolved PhotoemissionSpectroscopy. Phys. Rev. Lett. 96, 046411 (2006).58. Bian, G., Wang, X., Liu, Y., Miller, T. & Chiang, T. C. InterfacialProtection of Topological Surface States in Ultrathin Sb Films. Phys.Rev. Lett. 108, 176401 (2012).59. Saito, K., Sawahata, H., Komine, T. & Aono, T. Tight-binding theory ofsurface spin states on bismuth thin films. Phys. Rev. B 93 (2016).60. Randeria, M. T. et al. Ferroelectric quantum Hall phase revealed byvisualizing Landau level wavefunction interference. Nat. Phys. 14,796–800 (2018).61. Du, H. et al. Surface Landau levels and spin states in bismuth (111)ultrathin films. Nat. Commun. 7, 10814 (2016).62. Ohtsubo, Y. et al. Non-trivial surface-band dispersion onBi(111).N. J.Phys. 15, 033041 (2013).63. Wang, T., Yuan, N. F. Q. & Fu, L. Moiré Surface States and EnhancedSuperconductivity in Topological Insulators. Phys. Rev. X 11, 021024(2021).64. Cano, J., Fang, S., Pixley, J. H. & Wilson, J. H. Moiré superlattice onthesurfaceof a topological insulator.Phys.Rev.B103, 155157 (2021).65. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hallphase. Nature 452, 970–974 (2008).66. Kiesel, M. L., Platt, C., Hanke, W., Abanin, D. A. & Thomale, R.Competing many-body instabilities and unconventionalsuperconductivity in graphene. Phys. Rev. B 86, 020507 (2012).67. Toyama, H. et al. Two-Dimensional Superconductivity of Ca-IntercalatedGraphene on SiC: Vital Role of the Interface between MonolayerGraphene and the Substrate. ACS Nano 16, 3582–3592 (2022).68. Luo, Y. et al. A unique vanHove singularity in kagomesuperconductorCsV3-xTaxSb5 with enhanced superconductivity. Nat. Commun. 14,3819 (2023).69. Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F.Superconductivity in rhombohedral trilayer graphene. Nature 598,434–438 (2021).70. Yoshizawa, S. et al. Controlled modification of superconductivity inepitaxial atomic layer–organic molecule heterostructures. Nano Lett.17, 2287–2293 (2017).71. Fujimoto,S. ElectronCorrelationandPairingStates inSuperconductorswithout Inversion. Symmetry. J. Phys. Soc. Jpn 76, 051008 (2007).72. Gandhi, A. C. et al. Strong electron-phonon coupling insuperconducting bismuth nanoparticles. APL Mater. 7 (2019).73. Weitzel, B. & Micklitz, H. Superconductivity in granular systems builtfrom well-defined rhombohedral Bi-clusters: Evidence for Bi-surfacesuperconductivity. Phys. Rev. Lett. 66, 385–388 (1991).74. Yaji, K. & Tsuda, S. Development of a photoemission microscopyapparatus using a vacuum ultraviolet laser. e-J. Surf. Sci.Nanotechnol. 22, 46 (2023).75. Takamoto, S. et al. Towards universal neural network potential formaterial discovery applicable to arbitrary combination of 45 elements.Nat. Commun. 13, 2991 (2022).76. Ozaki, T. Variationally optimized atomic orbitals for large-scaleelectronic structures. Phys. Rev. B 67, 155108 (2003).77. Ozaki, T. &Kino,H.Numerical atomicbasis orbitals fromH toKr.Phys.Rev. B 69, 195113 (2004).https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 8www.nature.com/commsmat78. Ozaki, T. &Kino,H. Efficient projector expansion for the ab initio LCAOmethod. Phys. Rev. B 72, 045121 (2005).79. Lejaeghere, K. et al. Reproducibility in density functional theorycalculations of solids. Science 351, aad3000 (2016).AcknowledgementsWe thank S. Yoshizawa, F. Arai, S. Takezawa, H. Tanaka, A. Harasawa, andT. Iimori for their technical support during the STMandARPESexperiments.The computation in this work has been partly done using the facilities of theSuper-computer Center, the Institute for Solid State Physics, the Universityof Tokyo. This work was supported financially by JSPS KAKENHI (GrantNos. 20H05621, 22H01961, 20K15133, 22H01183, 23H03818, 23H04524),theWorld Premier International ResearchCenter (WPI) Initiative onMaterialsNanoarchitectonics, MEXT, Japan and the Innovative Science and Tech-nology Initiative for Security Grant Number JPJ004596, ATLA, Japan.Author contributionsT.N. and T.U. conceived the experiment, and T.N., T.U., K.Y. and Y.Y. wrotethemanuscript. T.N.,R.N. andW.Q.carriedout theSTMmeasurements, andT.N. analyzed the data. T.N., K.Y., Y.F., K.K., and R.M. carried out (S)ARPESmeasurements at ISSS under the supervision of T.K. Y.C., K.Y., and S.T.carried out (S)ARPES measurements at NIMS. K.Y. and S.T. analyzed theARPES/SARPES data. Y.Y. performed the DFT calculations. All the authorsdiscussed the results and contributed to finalizing the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s43246-024-00615-z.Correspondence and requests for materials should be addressed toTakashi Uchihashi.Peer review information Communications Materials thanks Baojie Fengand the other, anonymous, reviewer(s) for their contribution to the peerreviewof thiswork.PrimaryHandlingEditors:Dawei ShenandAldo Isidori. Apeer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as longas you give appropriate credit to the original author(s) and the source,provide a link to the Creative Commons licence, and indicate if changeswere made. The images or other third party material in this article areincluded in the article’s Creative Commons licence, unless indicatedotherwise in a credit line to the material. If material is not included in thearticle’sCreativeCommons licence and your intended use is not permittedby statutory regulation or exceeds the permitted use, you will need toobtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024https://doi.org/10.1038/s43246-024-00615-z ArticleCommunications Materials |           (2024) 5:167 9https://doi.org/10.1038/s43246-024-00615-zhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/commsmat Moiré superlattices of antimonene on a Bi(111) substrate with van Hove singularity and Rashba-type spin polarization Results Atomic structures: STM measurements Electronic structures: STS measurements Electronic structures: ARPES/ SARPES measurements Electronic structures: DFT calculations Discussion Methods Sample preparation STM measurements ARPES measurements DFT calculations Data availability References Acknowledgements Author contributions Competing interests Additional information