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[Satoru Ichinokura](https://orcid.org/0000-0002-7968-4016), [Shunsuke Tsuda](https://orcid.org/0000-0001-6209-8048), Kiyohisa Tanaka, [Koichiro Yaji](https://orcid.org/0000-0002-0721-1316)

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©2026 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Direct observation of the electronic structure of even-layer puckered SnTe monolayer films on graphene](https://mdr.nims.go.jp/datasets/70cf8783-39eb-4588-9dc1-467be665a216)

## Fulltext

Direct observation of the electronic structure of even-layer puckered SnTe monolayerfilms on grapheneSatoru Ichinokura,1, ∗ Shunsuke Tsuda,1 Kiyohisa Tanaka,2 and Koichiro Yaji1, 3, 41Center for Basic Research on Materials, National Institute for Materials Science, Tsukuba, 305-0003, Japan2UVSOR Synchrotron Facility, Institute for Molecular Science, Okazaki, 444-8585, Japan3Unprecedented-scale Data Analytics Center, Tohoku University, Sendai, 980-8578, Japan4Photon Science Innovation Center (PhoSIC), Sendai, 980-8572, JapanWe report a direct observation of the electronic structure of monolayer SnTe on graphene byangle-resolved photoemission spectroscopy. By combining low-energy electron diffraction, momen-tum microscopy, core-level spectroscopy, and first-principles calculations, we show that the observedmonolayer-limit electronic structure is consistent with a puckered even-layer biatomic-layer buildingblock rather than a nonpuckered square-flat structure. The observed band dispersion and its polar-ization dependence are reproduced by a puckered structure with a substrate-renormalized bucklingamplitude. We further show that graphene actively interacts with ultrathin SnTe by selecting itsin-plane orientational texture, renormalizing the buckling amplitude, and modifying the local in-terfacial electrostatic environment in the monolayer limit. In comparison, multilayer SnTe exhibitsa more ringlike momentum-space distribution, interlayer-split valence bands, and a stronger p-typecharacter, revealing the onset of thickness evolution from an interface-stabilized puckered ultrathinlimit toward a more bulklike state.Group-IV monochalcogenides and related ultrathinchalcogenide films, represented by MX (M = Ge, Sn;X = S, Se, Te), have emerged as an important class oftwo-dimensional materials because reduced dimensional-ity stabilizes low-symmetry puckered structures and am-plifies symmetry-breaking electronic responses. In thisfamily, the puckered distortion is a key ingredient thatdrives in-plane ferroelectricity, orbital anisotropy, and avariety of symmetry-enabled functionalities, as demon-strated experimentally in monolayer SnS, SnSe, and ul-trathin SnTe [1–4]. These symmetry-broken lattices fur-ther provide a fertile setting for spin-orbit-coupled andnonlinear phenomena, including Rashba-type spin split-ting, Berry-curvature dipoles, shift currents, and ultra-fast polarization control [5–10]. Related chalcogenidesystems such as GeTe have also highlighted how ferro-electricity can be directly coupled to spin texture control[11].Bulk SnTe, by contrast, adopts a high-symmetry rock-salt structure and, owing to its small band gap, is proneto band inversion and the emergence of topological crys-talline insulator (TCI) phases, as established on bothsingle crystals and thin films [12–15]. Indeed, if thelattice symmetry is retained down to the monolayerlimit, SnTe(001) has been predicted to realize a two-dimensional TCI [16, 17]. In practice, however, ultra-thin SnTe does not generically remain in this idealizedsquare-flat limit. Rather, as in other monochalcogenidesystems, a puckered structure built from biatomic lay-ers is energetically favored in the two-dimensional limit[4, 18]. Such a puckered phase is more naturally realizedas a larger-gap, symmetry-broken ferroelectric semicon-ductor and therefore lies outside the simple band-invertedTCI picture [6, 7, 19].∗ ICHINOKURA.satoru@nims.go.jpRecent work has shown that this balance can be shiftedby the substrate. In particular, trilayer-equivalent SnTeon NbSe2 has been reported to enter a two-dimensionaltopological crystalline insulating regime under substrate-induced compressive strain [20]. By contrast, grapheneinteracts much more weakly with SnTe and has beenshown by scanning tunneling microscopy studies to sup-port ultrathin SnTe in the ferroelectric limit with layeredantipolar ordering and domain formation [3, 4, 18, 21].However, direct determination by angle-resolved photoe-mission spectroscopy (ARPES) of whether the graphene-supported ultrathin limit realizes a puckered, symmetry-broken electronic structure rather than the idealized non-puckered picture invoked in simple two-dimensional TCIscenarios has remained unavailable.In this work, we directly determine the momentum-resolved electronic structure of monolayer-limit SnTe ongraphene. By combining ARPES with low-energy elec-tron diffraction (LEED), momentum microscopy, core-level spectroscopy, and first-principles calculations, weshow that the graphene-supported ultrathin limit real-izes a puckered even-layer biatomic-layer building blockrather than the idealized nonpuckered square-flat struc-ture invoked in simple two-dimensional TCI scenarios.We further show that graphene is not a passive sup-port: it selects the in-plane orientational texture, mod-ifies the lattice parameters relevant to the monolayerlimit, and changes the local interfacial electrostatic en-vironment. Finally, by comparing monolayer and multi-layer films, we identify the onset of thickness evolutionfrom an interface-stabilized puckered ultrathin limit to-ward a more bulklike regime.Ultrathin SnTe films were grown in situ on epitax-ial graphene formed on an n-type 4H-SiC(0001) sub-strate. The in-plane symmetry and reciprocal-space pat-tern were examined by LEED at an electron energy of74 eV. Constant-energy maps were measured by momen-© 2026 American Physical Society. This is the accepted manuscript of:S. Ichinokura et al., Phys. Rev. B 114, 165408 (2026).The final published version is available athttps://doi.org/10.1103/p3hj-vdc2.22UC(f) (g)Γ XY STop viewxy(a)Te2-Sn2+abSide view1UC(b)xzBZ(c)1UCPuckered Non-puckered(d) (e)Y Γ X SY Γ X S Y Γ X SΔxΔzY Γ X SWVBE B(eV)210-1-2-3-4E B(eV)210-1-2-3-4E B(eV)210-1-2-3-4E B(eV)210-1-2-3-4FIG. 1. Structural and electronic reference models for ul-trathin SnTe. (a),(b) Top and side views of the 2UC puck-ered structure. (c) Corresponding pseudotetragonal Brillouinzone. (d),(e) Calculated band structures of puckered and non-puckered 1UC SnTe. (f),(g) Calculated band structures ofpuckered and nonpuckered 2UC SnTe.tum microscopy using a 10.9 eV vacuum-ultraviolet lasersource [22–24]. Valence-band ARPES and Te 4d/Sn 4dcore-level spectra were measured at BL5U of UVSOR.Electronic-structure calculations were performed withindensity-functional theory (DFT) using fully relativis-tic projector-augmented-wave pseudopotentials and thePerdew–Burke–Ernzerhof generalized gradient approxi-mation. Further experimental and computational detailsare given in the Supplemental Material [25].Figure 1 introduces the structural and electronic ref-erence models used in this work. Figures 1(a) and 1(b)show the top and side views of the puckered structure,and Fig. 1(c) shows the corresponding pseudotetragonalBrillouin zone. Here, 1UC and 2UC denote one- andtwo-unit-cell-thick SnTe slabs, respectively.Using the relaxed 1UC puckered structure with a =4.560 Å and b = 4.530 Å, we obtain finite in-plane dis-placement and buckling, indicating that the puckeredstructure is energetically favored. For comparison, thenonpuckered reference calculations were performed withthe averaged in-plane lattice constant, a = b = 4.545 Å.TABLE I. Calculated structural parameters and band char-acteristics for the 1UC and 2UC SnTe models. ∆x: in-planeSn–Te displacement; ∆z: local buckling amplitude; WVB:valence-band width; ∆E: relative energy from the nonpuck-ered model at the same thickness.Layer Structure ∆x (Å) ∆z (Å) ∆E (meV/f.u.) WVB (eV)1UC Puckered 0.10 0.29 -20.2 1.1531UC Non-puck. 0 0 0 0.5902UC Puckered 0.15 0.22 -17.6 1.0352UC Non-puck. 0 0 0 0.660Graphene/SiC Multilayer SnTeMonolayer SnTe(c) (d) (e)(01)(11)a*Graa*SiC(11)(01)(10)(10)(a)SiCBufferGrapheneSnTe(b)60°30°ZigzagArmchair0°FIG. 2. LEED characterization of graphene-supported ultra-thin SnTe. (a) Schematic side view of the sample structureconsisting of SnTe on graphene/buffer/SiC. (b) In-plane ori-entation relationship between the pseudotetragonal SnTe lat-tice and the graphene lattice, illustrating domains rotated by0◦, 30◦, and 60◦. (c)–(e) LEED patterns of Graphene/SiC,monolayer SnTe, and multilayer SnTe, respectively, togetherwith schematic reciprocal-space patterns shown below.The calculated band structures of the puckered and non-puckered 1UC models are shown in Figs. 1(d) and 1(e),respectively. Compared with the puckered case, the non-puckered square-flat limit loses the weakly anisotropicvalence-band features.The 2UC results are shown in Figs. 1(f) and 1(g). Inthe puckered 2UC model, interlayer coupling increasesthe number of valence bands and produces a ladderlikestructure near Γ. The structural parameters and calcu-lated quantities are summarized in Table I. At both 1UCand 2UC thicknesses, the puckered structure is lower inenergy than the nonpuckered one, and the valence-bandwidth differs markedly between the two cases.Figure 2 summarizes the structural characterizationof graphene-supported ultrathin SnTe by LEED. Dur-3ing molecular beam epitaxy (MBE) growth, SnTe wasformed on graphene/buffer/SiC, as shown schematicallyin Fig. 2(a). The graphene/SiC substrate [Fig. 2(c)] ex-hibits the expected sixfold reciprocal-space features ofgraphene and SiC. After SnTe deposition, the monolayerfilm shows discrete SnTe-derived diffraction features, in-cluding the (01) and (11) spot arrays, that form an ap-parent 12-fold pattern [Fig. 2(d)]. This is naturally ex-plained by a superposition of pseudotetragonal domainswhose principal axes are locked to the graphene latticewith relative rotations of 0◦, 30◦, and 60◦ [Fig. 2(b)].From the LEED patterns, the in-plane lattice constantof SnTe is estimated to be 4.49 ± 0.02 Å for the mono-layer film and 4.44±0.02 Å for the multilayer film. Thesevalues are consistent with previous reports for monolayerSnTe and with the Te–Te distance of bulk cubic SnTe[3], and suggest a thickness-dependent relaxation towarda more bulklike in-plane lattice scale. In the multilayer[Fig. 2(e)], the same basic diffraction geometry is pre-served but the intensity becomes much more ringlike, in-dicating a broader orientational spread and/or increasedmosaicity. Thus, ultrathin SnTe on graphene is not asingle-domain crystal but a graphene-constrained mul-tidomain pseudotetragonal film, with the orientationallocking strongest in the monolayer limit.Figure 3 shows how this multidomain pseudotetrag-onal structure appears in momentum space and inthe valence-band dispersion. Figures 3(a)–3(c) presentconstant-energy maps near EF for Graphene/SiC, mono-layer SnTe, and multilayer SnTe, respectively. In theGraphene/SiC map, multiple Dirac-cone-like contoursare observed around Γ and are assigned to the well-knownreplica Dirac cones of graphene on SiC [26–28]. Becausethe same replica features are also visible in the monolayerdataset, we used them as internal references for the mo-mentum calibration of the momentum-microscopy maps.With this calibration, the monolayer map in Fig. 3(b)shows a set of SnTe-derived hole pockets in addition tothe graphene-derived replica features. As expected fromthe 1UC puckered model in Fig. 1(d), the valence-bandmaximum lies near the X point, and the superposition ofthe 0◦, 30◦, and 60◦ domains gives rise to the nearly12-fold pocket arrangement. By contrast, the multi-layer map in Fig. 3(c) retains the same basic momentum-space geometry but becomes much more ringlike, consis-tent with the broader orientational spread inferred fromLEED.The monolayer spectrum measured with p-polarizedlight [Fig. 3(e)] exhibits a relatively flat band near EB ∼1.0 eV hybridized with a V-shaped band. Since thevalence-band maximum remains near the Fermi level, theexperimental valence-band width is about 1.0 eV, smallerthan that of the fully relaxed freestanding puckered cal-culation in Fig. 1(d). We therefore first examined theeffect of the experimentally observed lattice compressionby fixing the in-plane lattice constants to the LEED valueof a = b = 4.49 Å and performing a structural optimiza-tion under this constraint. The resulting compression en-DFTΓX XE B(eV)pz px+pyMultilayer SnTeMonolayer SnTe(a) (b) (c)Γ XSYΓX XE B(eV)ΓX XE B(eV)p-pol.s-pol.(d) (e) (f)(g) (h) (i)ΓX XΓX Xhνpzxye-sE B(eV)E B(eV)p-pol.s-pol.Graphene/SiCΓ XSYkx (Å-1)k y(Å-1)1.00.50.0-0.5-1.01.00.50.0-0.5-1.0kx (Å-1)k y(Å-1)1.00.50.0-0.5-1.01.00.50.0-0.5-1.0ΓKkx (Å-1)k y(Å-1)1.00.50.0-0.5-1.01.00.50.0-0.5-1.0M0.0-1.0-2.00.0-1.0-2.00.0-1.0-2.00.0-1.0-2.00.0-1.0-2.0FIG. 3. Momentum-space electronic structure of graphene-supported ultrathin SnTe. (a)–(c) Constant-energy mapsnear the Fermi level for Graphene/SiC, monolayer SnTe, andmultilayer SnTe, respectively, measured by momentum mi-croscopy. In (b) and (c), pseudotetragonal Brillouin zones ofSnTe rotated by 0◦, 30◦, and 60◦ are overlaid. (d) Calculatedband structure of 1UC puckered SnTe for the experimentallyconstrained structure with a = b = 4.49 Å and a bucklingamplitude of 0.13 Å, with marker size and color represent-ing the Te pz and px + py orbital projections. (e),(h) Mono-layer ARPES spectra measured along X–Γ–X with p- ands-polarized light, respectively. (f),(i) Corresponding multi-layer spectra. (g) Experimental geometry for the polarization-dependent ARPES measurements.hances the buckling amplitude and drives the calculatedvalence-band width even farther away from the experi-mental value. We then reduced the buckling amplitudewithin the same constrained framework and found thata value of 0.13 Å provides the best match to the ex-perimentally relevant valence-band width (see Fig. S1 inthe Supplemental Material [25]). The recalculated bandstructure [Fig. 3(d)] agrees well with the ARPES disper-sion after aligning the flat-band energy.This agreement is not limited to the overall bandwidth.The constrained calculation with a buckling amplitude of0.13 Å also reproduces the observed polarization depen-dence: because p-polarized light contains an out-of-planeelectric-field component, the pz-derived part of the bandstructure is enhanced in Fig. 3(e), whereas the lower partof the V-shaped band becomes more pronounced with spolarization [Fig. 3(h)], consistent with stronger excita-tion of in-plane orbitals. Together with the calculationsin Fig. S2 of the Supplemental Material [25], this showsthat the flat band is mainly derived from pz orbitals, theV-shaped band from in-plane orbitals, and that spin–orbit coupling hybridizes them and opens the gap. We4(b) Sn 4d(a) Te 4dIntensity (a.u.)EB (eV) EB (eV)Intensity (a.u.)E B(eV)(d) w/ monolayer SnTeKE B(eV)(c) Graphene/SiCK(e) KΓBZGra(f)Graphenee-e-e-e-e-Sn2+Sn2+VSnTe2-Te2-Te-Te-e-Sn2+Te2-e-e- e- e-e- e-FIG. 4. Thickness-dependent core-level spectra and graphene-interface signatures in graphene-supported ultrathin SnTe.(a),(b) Te 4d and Sn 4d core-level spectra for monolayer andmultilayer SnTe. (c),(d) ARPES spectra near the grapheneK point before and after monolayer SnTe growth. The solidlines indicate EDCs taken at K. (e) Schematic of the grapheneBrillouin zone indicating the K point. The navy line denotesthe momentum cut used for the ARPES measurements in (c)and (d). (f) Schematic illustration of the proposed interfacialelectrostatic picture.therefore conclude that the monolayer film realizes theband structure of a 1UC puckered SnTe layer with a buck-ling amplitude reduced from the freestanding value, likelydue to the substrate effect. Because the Γ–X and Γ–Ydifferences are small and ferroelectric domains are mixedwithin the beam spot, this comparison is used to dis-tinguish between the puckered and nonpuckered modelsrather than to establish the in-plane anisotropy directly;direct verification of the in-plane anisotropy remains animportant subject for future domain-resolved measure-ments.For multilayer SnTe, the p-polarized ARPES spectrumin Fig. 3(f) exhibits a pronounced ladderlike structurearound Γ, qualitatively consistent with the splitting ofrelatively flat valence bands by interlayer coupling in the2UC model of Fig. 1(f). The corresponding s-polarizedspectrum in Fig. 3(i) emphasizes the more dispersive partof the valence band. In both monolayer and multilayerSnTe, the valence-band maximum lies very close to theFermi level, indicating strong hole doping.Figure 4 summarizes the thickness-dependent core-level behavior and interface-related signatures ingraphene-supported ultrathin SnTe. In the Te 4d spectra[Fig. 4(a)], the multilayer peak shifts to higher bindingenergy and becomes broader than the monolayer peak.This trend is consistent with the stronger intrinsic p-type character of thicker SnTe, for which Sn vacanciesare known to act as acceptor defects [29–31]. The broadermultilayer line shape further suggests a wider distributionof local Te environments, likely associated with defect-affected Te sites and interlayer-related chemical shifts.By contrast, the Sn 4d peak position changes onlyweakly with thickness, while its linewidth is slightlybroader toward the low-binding-energy side in the mono-layer [Fig. 4(b)]. This suggests that Sn 4d is less sensitivethan Te 4d to the thickness-dependent Sn-vacancy con-tribution, while in the monolayer limit it is affected by anadditional interface-specific effect, likely enhanced localscreening caused by the proximity of graphene.We also compared the graphene-derived spectra nearthe K point before and after monolayer SnTe growth[Figs. 4(c)–4(e)]. Within the uncertainty of the presentanalysis, no clearly resolvable shift of the graphene Diraccone is established. This argues against a substantial av-erage charge transfer from graphene into the SnTe film.Taken together with the Sn 4d line-shape broadening, thedata instead suggest that the graphene-induced electro-static effect is more likely a weak local screening at theinterface rather than a uniform doping of the SnTe layeras a whole.The overall picture is summarized in Fig. 4(f): thickerSnTe exhibits a stronger intrinsic p-type character,whereas in the monolayer limit the graphene interfacemainly affects the local electrostatic environment. Theprincipal substrate effects supported by the present dataare therefore the orientational locking, the renormaliza-tion of the buckling amplitude, and a weak interface-specific electrostatic screening in the monolayer limit.The results of Figs. 2–4 show that graphene is not apassive support for ultrathin SnTe, but actively stabi-lizes and renormalizes the monolayer limit. Structurally,LEED and momentum microscopy reveal that monolayerSnTe forms discrete domains locked to the graphene lat-tice, whereas the multilayer already develops a broader,more ringlike orientational distribution. Electronically,comparison between ARPES and DFT shows that themonolayer retains a puckered structure but with a re-duced buckling amplitude relative to the freestandingcase. In addition, the core-level analysis suggests a weakinterface-specific electrostatic screening in the monolayerlimit. Taken together, these results show that graphenecontrols the orientation and lattice distortion of ultrathinSnTe, while also modifying its local interfacial electro-static environment.The comparison between monolayer and multilayer fur-ther captures the onset of thickness evolution away fromthis interface-stabilized puckered limit. The multilayer5exhibits a more diffuse momentum-space distribution,interlayer-split valence bands, and a stronger p-type char-acter in both valence-band and core-level measurements.These trends indicate that the graphene-induced con-straints become weaker with increasing thickness, so thatthe film begins to recover a more intrinsic SnTe character.In this sense, the monolayer is the interface-stabilizedlimit, whereas the multilayer marks the beginning of acrossover toward a more bulklike, and possibly more β-like, state.In conclusion, we have established the electronic struc-ture of graphene-supported ultrathin SnTe from themonolayer to the multilayer regime. First, we achieved adirect momentum-resolved observation of the electronicstructure of monolayer SnTe. Second, the agreementbetween angle-resolved photoemission spectroscopy, po-larization dependence, and first-principles calculationssupports the assignment of the experimentally real-ized monolayer-limit electronic structure to a puckeredeven-layer biatomic-layer building block rather than anonpuckered square-flat limit. Third, we showed thatgraphene actively interacts with ultrathin SnTe by select-ing its in-plane orientational texture, renormalizing thebuckling amplitude, and modifying the local interfacialelectrostatic environment in the monolayer limit. Fourth,by comparing monolayer and multilayer films, we cap-tured the onset of thickness evolution from an interface-stabilized puckered ultrathin limit toward a more bulk-like, and possibly more β-like, state. These results iden-tify graphene-supported ultrathin SnTe as a platform inwhich puckering, substrate coupling, and thickness evo-lution can be directly resolved in momentum space.We thank S. Makita, F. Arai, F. Komori, N. Naga-mura, H. Ando, and H. Nomura for helpful discussions.We also thank H. Jin and J. Kim for providing thestructural models of SnTe. This work was supported byJSPS KAKENHI Grant No. JP24K01352, JST CRESTGrant No. JPMJCR2435, and the Shiraishi Founda-tion for Science and Development. Part of this workwas conducted at Nanofab, Science Tokyo, with supportfrom the Advanced Research Infrastructure for Materialsand Nanotechnology in Japan (ARIM), Grant No. JP-MXP1225IT0064.DATA AVAILABILITYThe data that support the findings of this article arenot publicly available. The data are available from theauthors upon reasonable request.[1] N. Higashitarumizu, H. Kawamoto, C.-J. Lee, B.-H. Lin,F.-H. Chu, I. Yonemori, T. Nishimura, K. Wakabayashi,W.-H. Chang, and K. Nagashio, Nature Communications11, 2428 (2020).[2] K. Chang, F. Küster, B. J. Miller, J.-R. Ji, J.-L. Zhang,P. Sessi, S. Barraza-Lopez, and S. S. P. Parkin, NanoLetters 20, 6590 (2020).[3] K. Chang, J. Liu, H. Lin, N. Wang, K. Zhao, A. 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Rev.Lett. 77, 3865 (1996).Supplemental Material for“Direct observation of the electronic structure of even-layer puckered SnTe monolayerfilms on graphene”Satoru Ichinokura,1, ∗ Shunsuke Tsuda,1 Kiyohisa Tanaka,2 and Koichiro Yaji1, 3, 41Center for Basic Research on Materials, National Institute for Materials Science, Tsukuba, 305-0003, Japan2UVSOR Synchrotron Facility, Institute for Molecular Science, Okazaki, 444-8585, Japan3Unprecedented-scale Data Analytics Center, Tohoku University, Sendai, 980-8578, Japan4Photon Science Innovation Center (PhoSIC), Sendai, 980-8572, JapanI. EXPERIMENTAL DETAILSUltrathin SnTe films were grown on epitaxial graphene formed on an n-type 4H-SiC(0001) substrate. Epitaxialgraphene was fabricated by annealing the SiC substrate at 1850◦C for 15 s in an Ar atmosphere at 800 Torr [32, 33].After degassing at 560◦C for 30 min, the graphene substrate was held at 200◦C, and SnTe was deposited from aKnudsen-cell source charged with SnTe powder [18]. Because SnTe was evaporated from a compound source ratherthan from separate elemental sources, Sn and Te were supplied simultaneously from the same Knudsen cell with thenominal stoichiometry of SnTe. The source material was 99.999% SnTe powder purchased from Kojundo ChemicalLaboratory Co., Ltd. All processes from film growth to LEED and photoemission measurements were carried out insitu in two separate systems: the LEED/momentum-microscopy apparatus and the UVSOR BL5U ARPES endstation,both equipped with growth chambers.To prepare well-separated thick-limit and thin-limit SnTe films in the two setups with different source–sampledistances, we used the same type of SnTe Knudsen-cell source and intentionally adopted sufficiently long and shortdeposition times in each system. In the UVSOR BL5U measurements, the thick-limit and thin-limit samples wereprepared with deposition times of 120 s and 12 s, respectively, whereas in the LEED/momentum-microscopy mea-surements the corresponding samples were prepared with deposition times of 3 min and 1 min.The successful preparation of the thick-limit and thin-limit samples was confirmed independently in the two systemsfrom the mutually consistent LEED patterns and ARPES spectra. The thick-limit samples exhibited ring-like LEEDpatterns and multilayer-type ARPES/Fermi-surface features, whereas the thin-limit samples showed the characteristicvalence-band dispersion of the monolayer regime. The thin-limit ARPES spectrum is reproduced well by the 1UCpuckered DFT calculation, confirming that the thin-limit sample corresponds to the 1UC SnTe regime. Accordingly,the monolayer and multilayer regimes in this work refer to these experimentally established thin-limit and thick-limitregimes, respectively.The in-plane crystallographic orientation, symmetry, and reciprocal-space pattern of the as-grown films were ex-amined by low-energy electron diffraction (LEED) using an electron energy of 74 eV.Constant-energy maps in momentum space were measured using a Nano-ESCA-based photoemission microscopyapparatus equipped with a 10.9 eV vacuum-ultraviolet laser [22–24]. The PEEM lens system enabled momentum-space (kx–ky) imaging, and the photoelectrons were energy-filtered with an Imaging Double Energy Analyzer (IDEA).The measurement temperatures were 44 K for the data shown in Fig. 3(a) and Fig. 3(b) in the main text, and 4 Kfor the data shown in Fig. 3(c).Valence-band ARPES and core-level photoemission measurements of Te 4d and Sn 4d were carried out at beamlineBL5U of the UVSOR synchrotron facility using an MBS A-1 analyzer [34]. The measurements were performed at9 K. For valence-band measurements, linearly polarized light with a photon energy of 65 eV was used, and both p-and s-polarized geometries were employed to distinguish the orbital contributions to the valence bands. For core-levelmeasurements, p-polarized light with a photon energy of 175 eV was used.II. COMPUTATIONAL DETAILSElectronic-structure calculations were carried out using QUANTUM ESPRESSO [35–37] within the framework ofKohn–Sham density functional theory [38, 39]. Fully relativistic projector-augmented-wave pseudopotentials were used∗ ICHINOKURA.satoru@nims.go.jp2Buckling amplitude Δz (Å)Valence band width WVB(eV)ARPESFIG. S1. Calculated valence-band width of monolayer SnTe as a function of the buckling amplitude ∆z, defined consistentlywith Table I. The calculations were performed with the in-plane lattice constant fixed to a = b = 4.49 Å. The dashed horizontalline indicates the experimental valence-band width of approximately 1.0 eV estimated from ARPES. The closest agreement isobtained for ∆z = 0.13 Å, which is therefore adopted in the main text as the substrate-renormalized buckling amplitude ofmonolayer SnTe on graphene.for Sn and Te, and the exchange-correlation functional was treated within the Perdew–Burke–Ernzerhof generalizedgradient approximation [40]. The plane-wave cutoff energies for the wave functions and charge density were setto 50 and 250 Ry, respectively. Spin–orbit coupling was included within the noncollinear formalism. Structuralrelaxation was performed using the Broyden–Fletcher–Goldfarb–Shanno algorithm with a force convergence thresholdof 1.0×10−3 and an electronic convergence threshold of 1.0×10−6, using a 6×6×1 k-point mesh. A vacuum spacingcorresponding to a c-axis lattice parameter of 21.5615 Å was introduced in the slab geometry.For the spin–orbit-coupled band-structure calculations of the puckered and non-puckered models shown in Fig. 1of the main text, self-consistent calculations were carried out on a 12× 12× 1 k-point mesh with Methfessel–Paxtonsmearing of 0.02 Ry, followed by band calculations along the Y–Γ–X–S high-symmetry line. For the puckered model[Fig. 1(d),(f)], the lattice parameters were a = 4.560 Å, b = 4.530 Å, and c = 21.5615 Å. For the non-puckeredmodel [Fig. 1(e),(g)], the in-plane lattice constants were fixed to the average value of the puckered model, namelya = b = 4.545 Å. To retain the inversion-symmetry-broken spin splitting, both nosym=.true. and noinv=.true.were imposed.For the experimentally constrained calculation shown in Fig. 3(d), the in-plane lattice constants were fixed to theexperimental monolayer value, a = b = 4.49 Å.For the orbital-character analysis in Fig. 3(d) of the main text, a separate calculation sequence was employed usinga structure constrained to a = b = 4.49 Å with a fixed buckling amplitude of 0.13 Å, while only the in-plane atomicpositions were relaxed. A subsequent self-consistent calculation was then performed, followed by projection analysisusing projwfc.x. Because the spin–orbit-coupled projections are obtained in the j,mj basis, the resulting complexprojection amplitudes were further transformed into out-of-plane pz and in-plane (px + py) components using theClebsch–Gordan decomposition for comparison with polarization-dependent ARPES.3pz pxE B(eV)FIG. S2. Orbital-projected band structure of monolayer puckered SnTe calculated without spin–orbit coupling for the sameconstrained structure used in the main text. The marker size indicates the projection onto Te pz (magenta) and in-plane px(green) orbitals. In the absence of SOC, the relatively flat pz-derived band and the dispersive in-plane band cross along X–Γ–X.In the SOC-included calculation and in the ARPES data shown in the main text, this crossing evolves into an anticrossing,demonstrating SOC-induced hybridization between the two orbital sectors.III. SUBSTRATE-RENORMALIZED BUCKLING OF MONOLAYER SNTETo further quantify the substrate-limited buckling discussed in the main text, we performed additional DFT calcu-lations while fixing the in-plane lattice constant to the experimental value of a = b = 4.49 Å and varying the bucklingamplitude ∆z stepwise. Here, ∆z is defined in the same manner as in Table I, namely, as the vertical separationwithin an Sn–Te pair relative to the pair-averaged plane. For each constrained structure, the valence-band widthwas extracted from the calculated band dispersion in the same manner as in the main text. As shown in Fig. S1,the calculated valence-band width increases monotonically with increasing ∆z. Comparing these values with theexperimental bandwidth of approximately 1.0 eV obtained from ARPES, we find that the best agreement is obtainedfor ∆z = 0.13 Å. This result supports the interpretation that monolayer SnTe on graphene retains a puckered struc-ture, but with a reduced buckling amplitude compared with the fully relaxed freestanding structure. The value of∆z = 0.13 Å should therefore be regarded as a semi-quantitative estimate of the experimentally relevant buckling scalewithin this constrained Perdew–Burke–Ernzerhof (PBE) framework, rather than as a unique structural determinationbased solely on the absolute calculated bandwidth.IV. ORBITAL CROSSING WITHOUT SPIN–ORBIT COUPLINGTo clarify the role of spin–orbit coupling (SOC) in the monolayer band structure, we also calculated the orbital-projected band dispersion without SOC for the same constrained puckered structure with a = b = 4.49 Å and∆z = 0.13 Å used in the main text. As shown in Fig. S2, the relatively flat pz-derived band and the more dispersivein-plane px-derived band cross each other along X–Γ–X when SOC is neglected. In contrast, the SOC-includedcalculation shown in the main text exhibits a clear avoided crossing between these two bands. The ARPES spectralikewise show the hybridized, anticrossing band structure rather than a simple crossing. 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