Dimensional crossover and band topology evolution in ultrathin semimetallic NiTe2 films

Nickel ditelluride (NiTe2), a recently discovered Type-II Dirac semimetal with topological Dirac fermions near the Fermi energy, is expected to exhibit strong thickness-mediated electronic tunability and intrinsic two-gap superconductivity in the single-layer limit. Realizing such intriguing phenomena requires the fabrication of ultrathin NiTe2 films and an understanding of the underlying physics that is still under debate. By conducting experimental band mappings of ultrathin films prepared with molecular beam epitaxy, we reveal spectroscopic evidence for the dimensionality crossover of single-crystalline ultrathin NiTe2 films as a function of film thickness. As the film thickness increases from one to five layers, the gap in the conical topological surface states closes. Comparisons of experimental to first-principles results also highlight difficulties in fabricating atomically smooth single-layer NiTe2 films. Our results not only provide further impetus for studying emergent phenomena in NiTe2 but also underscore the limitations of fabricating NiTe2 films for device applications.


INTRODUCTION
Recent years have beheld the emergence of transition metal dichalcogenides (TMDCs) as a rich class of quasi-two-dimensional materials with electronic properties spanning from trivial semiconductors and semimetals to superconductors and topological phases [1][2][3] . By virtue of the weak van der Waals bonding between layers, these materials can usually be isolated into single-layer phases [4][5][6][7][8][9][10][11][12][13][14] and can sometimes be perfect testing grounds for probing phenomena modified from or distinct from the bulk limit, including quantum spin Hall systems 6,7 , superconductivity [8][9][10] , charge density wave (CDW) phases [11][12][13] , and semiconductor-tosemimetal transitions 14 . Specific cases include a direct gap semiconductor phase in MoS 2 and WS 2 in the single-layer limit 4,5 , CDW phases in single-layer TiTe 2 and VSe 2 distinct from bulk phenomena 12,13 , and recently, a strong thickness-mediated Lifshitz transition from a semimetal to a semiconductor phase in ultrathin PtTe 2 films 14 . The Ni-based TMDC NiTe 2 is also ideal for exploring unusual phenomena in bulk and at reduced dimensions [15][16][17][18][19][20][21][22][23][24] . Though bulk NiTe 2 is not superconducting, ab initio calculations have predicted an intrinsic two-gap superconducting state in single-layer NiTe 2 with a transition temperature T c~5 .7 K (ref. 17 ). In addition, bilayer NiTe 2 intercalated with an alkali metal may be a two-gap superconductor with a gap as high as~3.1 meV and a critical temperature T c~1 1.3 K (ref. 17 ). Moreover, recent work on NiTe 2 under high pressure has shown the onset of superconductivity at small pressures and a second superconducting phase at even higher pressures with a transition temperature T c~7 .5 K (ref. 18 ), implying that NiTe 2 is near the threshold of a superconducting instability. Ferromagnetic ordering at low temperatures with a Curie temperature T F~2 2 K has also been found in NiTe 2 nanostructures 20 , but bulk NiTe 2 itself is paramagnetic 21 .
Furthermore, NiTe 2 is a candidate for the Type-II topological Dirac semimetal phase [21][22][23][24] , in which low-energy excitations of emergent Dirac fermions generate a strongly tilted bulk Dirac cone that breaks Lorentz symmetry [21][22][23][24][25][26][27][28][29][30][31] . Such symmetry breaking should generate electronic and physical properties distinct from other topological semimetals, including an anisotropic magnetoresistance and chiral anomaly [28][29][30][31][32] and unconventional superconductivity 21,33 . The topological nature of bulk NiTe 2 single crystal has been addressed recently through both spin-resolved and conventional angle-resolved photoemission spectroscopy (ARPES), which revealed evidence for a topological Dirac cone with spin-polarized surface states at an energy E~−1.4 eV and a Type-II Dirac node near the Fermi level at E = 0 eV (refs. 23,24 ). The results contrast from the Pt-and Pd-based topological semimetals, which have Type-II Dirac cones located very far from the Fermi level at energies E~−0.6 eV to −1.2 eV (refs. [25][26][27][28][29]. Thus, in lieu of the Pt-and Pd-based systems, NiTe 2 is likely an improved platform for exploiting topological Dirac fermions and other emergent phenomena for the development of spintronic or topological devices. However, to realize such physics, the thicknessdependent electronic band structure of ultrathin NiTe 2 films needs to be fully addressed, a prerequisite for revealing the system's electronic tunability in the ultrathin-film limit and for further assessing the feasibility of fabricating atomically smooth NiTe 2 films in a device setting. Here, we present ARPES band mappings of ultrathin, semimetallic NiTe 2 films of nominal thicknesses 1-5 triatomic layers (TL) fabricated using molecular beam epitaxy (MBE) on bilayergraphene-terminated surfaces, which provide clear spectroscopic evidence of strong thickness-mediated electronic tunability of NiTe 2 films. Specifically, our detailed band maps for increasing film thickness show the closing of the hybridization gap in the topological surface Dirac cone already at 5 TL in thickness and simultaneously, the development of linear-like bands near the Fermi level attributable to the lower branches of the Type-II Dirac cone in the bulk limit 23,24 , both indicative of the dimensionality crossover from the ultrathin-film to bulk-like regimes. Our results also suggest that NiTe 2 is a robust semimetal even in the singlelayer limit, contrasting from the semiconducting behavior in 1 TL PtTe 2 (refs. 14,34 ). Furthermore, first-principles calculations of NiTe 2 based on density functional theory (DFT) are compared with the measured ARPES spectra to confirm the fabrication of singlecrystalline NiTe 2 films in only the 1 T phase and thus to dismiss the question of another stable phase, such as the pyrite lattice [35][36][37] , appearing in our results. However, we discover that atomically smooth NiTe 2 films grown with MBE on bilayer graphene are seemingly unstable in the ultrathin-film regime, raising potential serious questions about the feasibility of integrating smooth one TL NiTe 2 films in a device and highlighting possible difficulties in observing emergent phenomena in 1 and 2 TL systems.

RESULTS AND DISCUSSION
Growth and characterizations of 1+2 TL and 5 TL 1 T NiTe 2 NiTe 2 has been suggested to exist in multiple lattice structures, including the 1 T and pyrite lattices (refs. [15][16][17][18][19][20][21][22][23][24][35][36][37] ) (see Fig. 1a and Supplementary Fig. 1). We confirm that NiTe 2 can adopt in theory four distinct phases: 1 T, 2H, pyrite, and marcasite, whose lattice structures and corresponding bulk Brillouin zones all appear in Supplementary Fig. 1. Table 1 summarizes each of their normalized energy per unit cell, which reveals that the 1 T phase has the lowest energy, followed by the marcasite and pyrite lattices, and is thus the most energetically stable phase. Figure 1a presents the atomic lattice structure for 1 TL of 1 T NiTe 2 , which contains three triangular atomic layers of Te and Ni stacked in the order Te-Ni-Te. The bulk lattice for 1 T NiTe 2 is assembled by vertically stacking many of these TLs directly on one another, each separated by a lattice constant c = 5.26 Å, with no other rotational and translational offsets, and van der Waals bonded with neighboring layers. The corresponding (001)-projected surface Brillouin zone is displayed in Fig. 1b. In this work, ultrathin 1 T NiTe 2 films with thicknesses N = 1-5 TL are grown on bilayergraphene-terminated 6H-SiC(0001) surfaces (BLG-SiC). Representative in situ reflection high-energy electron diffraction (RHEED) patterns for a BLG-SiC surface and a 5 TL film are shown in the left and right panels of Fig. 1c, respectively; the sharp diffraction streaks for the 5 TL film are evidence of a highly well-ordered surface.
An overview ARPES spectra and a zoomed-in view of the same band map for a 1+2 TL 1 T NiTe 2 film taken along the ΓM direction, where "1+2 TL" means a film with a mixture of 1 and 2 TL ARPES signal, are displayed in the left and right panels of Fig. 1d, respectively. The corresponding calculated DFT band structure, consisting of the calculation for a 1 TL film (red curves) superimposed with that of a 2 TL film (blue curves), appears in Fig. 1e. Similar ARPES and theoretical results for a 5 TL film, which we find are in the bulk-like regime, are summarized in Fig. 1f and g, respectively. Evidently, the electronic band structure in Fig. 1d consists of a mixture of 1 and 2 TL signal, though the film thickness based upon the amount of deposition should be 1 TL. Incidentally, reduction of the calibrated film thickness from 1 TL to 0.5 TL in thickness, the former being the result shown in Fig. 1d, yields similar ARPES band maps as in Fig. 1d with faint bands arising from a 2 TL film thickness. For example, from the red theoretical curves in Fig. 1e, the band structure of 1 TL 1 T NiTe 2 should be a relatively simple, robust semimetal with only three bands crossing the Γ point in the energy range E = 0 to −2 eV and a negative gap of~−0.50 eV (see, for instance, Supplementary  Fig. 4), quite unlike its Pt-based counterpart that is semiconducting at this thickness 14,34 . However, in the ARPES results in Fig. 1d, an additional weak band crosses at the Γ point at E~−0.5 eV (indicated by a red arrow in Fig. 1d), which can be ascribed to that of a 2 TL film thickness (compare to the blue curves in Fig. 1e). Furthermore, as the bands disperse along the ΓM direction away from the Γ point, additional bands not belonging to the 1 TL system can be duly assigned to those of a 2 TL film. The situation for the 5 TL sample is a bit different from the 1 + 2 TL system ( Fig. 1f, g). Generally speaking, the first-principles calculation result in Fig. 1g is more representative of the 5 TL ARPES map in Fig. 1f with the effects of any layer mixing less obvious at this thickness and is thus in accord with our expected thickness calibration. In other words, our results suggest that it is difficult to prepare a uniform 1 T NiTe 2 thin film on BLG-SiC, implying enhanced interlayer coupling relative to the Pt-based topological semimetals 14 . Since we observe 1 + 2 TL and 5 TL band structures in our ARPES results (see Fig. 1d, f), though we expect 1 TL and 5 TL signals, respectively, based on our thickness calibration, the surface energy of the BLG-SiC substrate, while conducive for fabricating other single-layer TMDC films 6,7,10-14 , may be too low for forming a uniform 1 TL 1 T NiTe 2 film. Rather, the next TL starts forming over the first TL well before the BLG-SiC surface is fully covered. Clean layer-resolved evolution of the band structure using ARPES at film thicknesses such as 1 and 2 TL may thus be potentially problematic, which can complicate observation of emergent phenomena, such as two-gap superconductivity, in this thickness regime and possibly integration of 1 T NiTe 2 in a device setting.
Gap opening in topological states at reduced thickness Despite these difficulties in realizing pure 1 TL and 2 TL systems, the results highlight a clear departure in the electronic band structures between films grown at low coverages and those in the bulk-like limit, which arises from quantum confinement along the surface normal. In particular, the band dispersions of the conical topological surface states (TSS) (refs. 23,24 ), labeled as TSS in Fig. 1d, f, are modified as the thickness is reduced from 5 TL to 1+2 TL. Figure 2a displays the ARPES spectra taken along ΓM (left panel) and the same map zoomed-in around the TSS (right panel) for a 1+2 TL 1 T NiTe 2 film; the corresponding second-derivative maps are displayed in Fig. 2b, whereas similar ARPES and secondderivative spectra for the 5 TL film appear in Fig. 2c and d, respectively. These results are very clear: At 1+2 TL in thickness, a hybridization gap of E g~0 .1 eV opens in the conical TSS (right panels of Fig. 2a, b), typical of ultrathin topological films driven by quantum-mechanical coupling between the film's two boundaries 38,39 , but for a 5 TL film, the gap in these surface states is not present within the experimental energy resolution (right panels of Fig. 2c, d). Furthermore, in the ARPES spectra for the 5 TL sample, linear bands that seemingly connect at or slightly above the Fermi level (identified by the label DB in the right panel of Fig. 1f) are present near the zone center, which in the bulk limit, are attributable to the lower branches of a bulk Type-II Dirac cone 23,24 , but for the 1+2 TL film, these bands are entirely absent. The ARPES map for the 5 TL sample is also much more complicated than the 1+2 TL film at the zone center, with a dense set of upside-down U-shaped bands appearing near the Γ point in the energy range E = −0.25 to −1 eV (Fig. 1f, g); these bands are mostly lacking in the 1+2 TL case (Fig. 1d, e). Generally, the results for the 5 TL sample are consistent with those previously reported for bulk 1 T NiTe 2 single crystal with a Type-II Dirac node near the Fermi energy 23,24 , though the film has not reached the bulk limit as evidenced by the discretization of the bulk occupied states into quantum well bands in the ARPES and theoretical results.
Dimensionality crossover in the band maps of 1 T NiTe 2 films The thickness dependence of 1 T NiTe 2 films from the ultrathinfilm to bulk-like limit is of fundamental interest to reveal how the band structure of 1 T NiTe 2 evolves into a bulk Type-II Dirac semimetal system with topologically protected nontrivial states. ARPES band maps and their second-derivative spectra for ultrathin 1 T NiTe 2 films of nominal thicknesses N = 1-5 TL taken along the ΓM direction are summarized in Fig. 3a and b, respectively. Figure  3c displays the corresponding DFT calculations, whereas ARPES maps in Fig. 3d are overlaid with the same theoretical results to foster further comparisons. A similar data set for the thicknessdependent band structure along the ΓK direction appears in Fig. 4. Some general comments about the bulk-like and ultrathin-film regimes are warranted for these results. None of these band maps show any evidence of other phases aside from 1 T NiTe 2 (see Supplementary Figs. 3 and 4), and all of these thin-film samples are semimetallic. For all thicknesses <5 TL, the conical TSS at E− 1.45 eV in the 5 TL system are gapped. As the thickness increases from 1 to 5 TL, this hybridization gap becomes smaller and first closes at 5 TL in thickness, signaling the onset of the bulk-like limit. A 5 TL film is thus the critical thickness for realizing such a topologically protected surface Dirac cone with spin-polarized surface states 23,24 . As discussed previously, the 5 TL film also shows incipient hints of the lower branches of the Type-II Dirac cone (Figs. 1f, 3, and 4). When the film thickness is reduced from 5 TL to 4 TL, this structure mostly disappears, with fewer bands crossing the Fermi level near the zone center (compare Figs. 1f, 3, and 4); no bands cross the Γ point very close to the Fermi level for the 1+2 TL and 3 TL samples, and the structure for the Type-II Dirac cone is entirely absent. Such observations alone are indicative of the strong thickness-mediated tunability of the band structure for 1 T NiTe 2 .
The discussion can be generalized even further for other occupied bands in this system. Per the results in Figs. 3 and 4, an increase in the 1 T NiTe 2 film thickness from one thickness to the next necessarily results in the multiplication of quantum well bands, which is well-known in noble metallic films 40 . For example, in the spectra in Figs. 3a, b and 4a, b, we see that the number of upside-down U-shaped bands at the zone center in the energy range E = −0.2 to −1 eV increases by exactly one as the thickness is tuned from 3 TL to 4 TL. However, increasing the thickness to 5 TL results in an even denser set of these U-shaped bands, and though resolvable, it starts becoming more difficult to count these bands separately as the film is approaching the bulk limit. Corresponding statements for band counting can be duly noted for occupied bands away from the Γ point. Similar evolution of the band structure has been reported for the Pt-based topological semimetals 14 . However, unlike their Pt-based counterparts 14 , for all NiTe 2 thin films measured here, the second-derivative ARPES maps (Figs. 2b, d, 3b, and 4b) tend to exhibit a very small amount of signal from the next layer owing to the presence of other minor thicknesses arising from the growth process, though such an effect is less apparent as the film thickness increases to 4 TL or 5 TL. Nevertheless, when these observations are taken into account, the calculation results are in general agreement with the measured ARPES spectra, with minor discrepancies not unusual from first-principles calculations.
Synchrotron Fermi surface maps for 3-5 TL 1 T NiTe 2 films At last, Fig. 5a and b display the measured Fermi surface maps and their corresponding second derivatives for N = 3-5 TL 1 T NiTe 2 thin films, respectively; the calculated Fermi surface maps are shown in Fig. 5c for comparison. Superficially, the three sets of experimental Fermi surface contours for 1 T NiTe 2 near the zone center are similar to one another in this thickness regime, but there are clear notable differences. One particular change occurs within a small, seemingly circular pocket centered about the Γ point, which is indicated by a white arrow in each secondderivative map in Fig. 5b. Within this circle, another small circular pocket develops prominently as the thickness increases from 3 TL to 4 TL (indicated by a red arrow in the 4 TL map in Fig. 5b). Upon further increase to 5 TL in thickness, it is replaced by an even tinier pocket or dot (designated by a yellow arrow in the 5 TL map in Fig. 5b). Aside from these changes, the Fermi surface contours themselves become denser and thus more complex with increasing film thickness, as expected for films at larger thicknesses. At some point, these contours should converge to  the bulk Fermi surface map, modulated by ARPES matrix element effects. These changes are further illuminating in regards to the thickness-mediated crossover of 1 T NiTe 2 from the ultrathin-film to a bulk-like limit reminiscent of the Type-II Dirac semimetal phase. From Figs. 3 and 4, no bands are present near the zone center at the Fermi level for a 3 TL film, but when the thickness is increased to 4 TL, another set of hole-like bands centered about the Γ point develops. Evidently, this should correspondingly cause a smaller hole pocket to arise in the Fermi surface map, which is indeed seen in the 4 TL maps in Fig. 5 (indicated by the red arrow in the middle panel of Fig. 5b). A further increase in the film thickness to 5 TL causes the bands near the Fermi level at the Γ point to become very dense, such that the Fermi level now crosses a tiny conical band very close to its apex (see right panel of Fig. 1f and also Figs. 3 and 4). The experimental Fermi surface map for the 5 TL sample should have a very tiny pocket or dot at the zone center, which is evident in the experimental result for the 5 TL film in Fig. 5 (identified by the yellow arrow in the right panel of Fig. 5b). In other words, the results for the Fermi surface maps provide additional confirmation of the crossover from the ultrathin-film to bulk-like limit as the film thickness is increased and thus corroborate with our analysis related to Figs. 3 and 4.

DISCUSSION
Our comprehensive experimental and theoretical efforts demonstrate that we have successfully fabricated ultrathin films of 1 T Fig. 3 Thickness-dependent ARPES spectra taken along the ΓM direction. a ARPES band maps of 1-5 TL 1 T NiTe 2 films measured with 21.218-eV photons at 30 K; those bands that are conical topological surface states in the bulk limit are labeled as TSS in the 5 TL map. b Corresponding second-derivative ARPES maps. c Corresponding calculated DFT band structures; in the calculation for the 1+2 TL case, the red curves correspond to the results for a 1 TL sample, whereas the blue curves are associated with those of a 2 TL film. d Layer-dependent ARPES spectra from a overlaid with the same calculation results from c; in the results for the 1+2 TL system, the white dashed curves are associated with the 1 TL calculation and those of a 2 TL film correspond with the pink dashed curves. NiTe 2 with thicknesses N = 1-5 TL on BLG-SiC using MBE, a system expected to exhibit emergent, intrinsic superconductivity in the 1 TL limit and also a topological Type-II Dirac fermion phase in bulk. By employing DFT first-principles calculations, we completely dismiss any mixture of other phases, including pyrite and marcasite NiTe 2 , in our ARPES band maps. These results together are spectroscopic evidence for the strong thickness-mediated electronic tunability of 1 T NiTe 2 , revealing the crossover from the ultrathin-film to bulk-like limit with incipient hints of the Type-II Dirac semimetal phase with bulk Dirac fermions near the Fermi level. Our experimental ARPES maps specifically show that the hybridization gap in the topological surface Dirac cone at an energy E~−1.45 eV first closes at 5 TL in thickness. Nevertheless, despite these successes, we discover that as-grown ultrathin 1 T NiTe 2 films favor growing in an approximately layer-by-layer manner on BLG-SiC, suggesting enhanced interlayer coupling in this system relative to the Pt-based topological semimetals. Finally, DFT calculations and the measured ARPES spectra are in good agreement with one another. Future studies into this system may wish to instead employ local probes, such as scanning tunneling spectroscopy (STS), to characterize the electronic structure of ultrathin 1 T NiTe 2 films further and to confirm or refute superconductivity in the 1 TL 1 T NiTe 2 system. For such works, substrates other than BLG-SiC may also be more conducive for growth of atomically smooth 1 TL 1 T NiTe 2 films, which would engender further assessments regarding the fabrication and suitability of 1 TL films for technological applications. We overall expect that these findings help complete the picture for ultrathin b Corresponding second-derivative ARPES maps. c Corresponding calculated DFT results; in the calculation results for the 1+2 TL system, the red curves are those for a 1 TL film, and the blue curves correspond to the results for a 2 TL film. d Thickness-dependent ARPES maps from a superimposed with the same calculation data from c; for the 1+2 TL system, the white dashed curves are for the 1 TL result, whereas those of a 2 TL film correspond to the pink dashed curves.
films whose bulk phase is a Type-II Dirac semimetal and also underline potential difficulties in employing MBE-grown 1 T NiTe 2 films in a device setting.

Sample preparation of 1 T NiTe 2 films
Prior to growth of ultrathin NiTe 2 films via MBE at the University of Illinois, 6H-SiC(0001) substrates were degassed at~500°C for a couple hours and then flash annealed to~1300°C for more than 50 cycles, yielding wellordered bilayer-graphene-terminated surfaces 41 . High-purity Ni and Te were co-evaporated from an electron-beam evaporator (Ni) and an effusion cell (Te) onto a BLG-SiC surface maintained at 280°C. The film growth rate was 1 TL (1 TL ≈ 0.5 nm) every~50 min. Following the film growth, sample quality was confirmed in situ using RHEED and ARPES. Photoemission measurements at the University of Illinois were performed at 30 K using a Scienta Omicron VUV5k He discharge lamp coupled with a Scienta R4000 hemispherical analyzer. Each NiTe 2 film was capped with a 10-nm-thick Te film to preserve surface integrity upon removal from the ARPES system. These samples were taken to Beamline 10.0.1.1 (HERS) at the Advanced Light Source (ALS) for additional ARPES characterizations. They were decapped in ultra-high vacuum by heating under Te flux tõ 300°C just prior to the measurements. The synchrotron results were obtained at a sample temperature of~80 K and an overall energy resolution better than 15 meV. In addition to the results outlined in the main discussion, constant energy contour maps E(k x , k y ) obtained at synchrotron for 1 T NiTe 2 thin films of thicknesses 3-5 TL are briefly considered in Supplementary Note 5 and Supplementary Fig. 22, whereas additional analysis and processing of data taken at the University of Illinois are detailed in Supplementary Note 6 and Supplementary Figs. 23-25.

First-principles calculations
First-principles calculations were conducted in the DFT framework 42 as implemented in the Vienna ab initio simulation package 43 ; the projected augmented wave approach was employed with an energy cutoff of 400 eV (refs. 44,45 ). To replicate the experimental lattice constants, the optB86b-vdW functional 46 for the van der Waals correction was used for the structural relaxation, such that the residual force on each atom was <10 −3 eV/Å; the self-consistent convergence criterion was set to 10 −5 eV. Thin films were modeled as a periodic array of finite-layer systems, each Thickness-dependent Fermi surface contours for 3-5 TL 1 T NiTe 2 . a Measured Fermi surface maps taken using 54-eV photons at a sample temperature of 80 K. b Corresponding second-derivative maps. As discussed in the main text, the white arrow in each panel refers to the circular pocket centered at the zone center common to all of these film thicknesses, whereas the red and yellow arrows identify pockets distinct to the 4 TL and 5 TL systems, respectively, that arise as the thickness is varied. c Corresponding calculated Fermi surface contours; the Fermi level of the system was shifted slightly by −0.071 eV for better agreement with the experimental results. separated from one another by a vacuum gap of 15.0 Å. For thin films, the first Brillouin zone was sampled by employing Γ-centered Monkhorst-Pack (ref. 47 ) k-space meshes of 24 × 24 × 1, whereas for bulk structures, k-space meshes of 24 × 24 × 12, 24 × 24 × 6, and 24 × 24 × 18 for the 1 T, 2H, and orthorhombic (pyrite and marcasite) structures were utilized, respectively. SOC was included in the theoretical band structures presented, unless indicated otherwise. The lattice structures and select theoretical band structure results for 1 T, 2H, pyrite, and marcasite phases of NiTe 2 are considered in Supplementary Note 1 and Supplementary Figs. 1-4. Additional calculations that employ the generalized gradient approximation (GGA) with a Hubbard-like onsite Coulomb repulsion correction (GGA+U) (refs. 48,49 ) and the metaGGA SCAN functional 50 for 1 T NiTe 2 thin films are codified in Supplementary Note 2 and Supplementary Figs. 5-10. Theoretical discussions relevant to the recently predicted superconductivity and magnetic ordering in 1 TL 1 T NiTe 2 (refs. 17,19 ) and the spin polarization of the TSS as a function of film thickness are outlined in Supplementary Notes 3 and 4, respectively, the results of which are further detailed in Supplementary Figs. 11-21 and Supplementary Tables 1-3.

DATA AVAILABILITY
All data needed to evaluate the conclusions in the paper are included in the paper and/or the Supplementary Information. Additional data related to this paper may be requested from T.C.C. (tcchiang@illinois.edu) and F.C.C. (fchuang@mail.nsysu.edu.tw).