Evidence of Topological Edge States in Buckled Antimonene

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Evidence of topological edge states in buckled antimonene monolayers Shi-Yu Zhu, Yan Shao, En Wang, Lu Cao, Xuan-Yi Li, Zhong-Liu Liu, Chen Liu, Liwei Liu, Jiaou Wang, Kurash Ibrahim, Jia-Tao Sun, Yeliang Wang, Shixuan Du, and Hong-Jun Gao Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b02444 • Publication Date (Web): 21 Aug 2019 Downloaded from pubs.acs.org on August 21, 2019

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Evidence of topological edge states in buckled antimonene monolayers Shi-Yu Zhu,†,# Yan Shao,†,# En Wang,†,# Lu Cao,† Xuan-Yi Li,† Zhong-Liu Liu,† Chen Liu,|| Li-Wei Liu,‡ Jia-Ou Wang,|| Kurash Ibrahim,|| Jia-Tao Sun,†,‡,* Ye-Liang Wang,†,‡,§,* Shixuan Du,†,§ and Hong-Jun Gao,†,§,* †

Institute of Physics and University of Chinese Academy of Sciences, Chinese Academy of Sciences,

Beijing 100190, China. ‡

School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China.

§ CAS ||

Center for Excellence in Topological Quantum Computation, Beijing 100049, China.

Institute of High-Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

Corresponding Author: Jia-Tao Sun,

Email: [email protected],

Tel: +86-10-82649881

Ye-Liang Wang, Email: [email protected], Tel: +86-10-68912993 Hong-Jun Gao,

Email: [email protected],

Tel: +86-10-82648035

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ABSTRACT: Two-dimensional topological materials have attracted intense research efforts owing to their promise in applications for low-energy, high-efficiency quantum computations. Group-VA elemental thin films with strong spin-orbit coupling have been predicted to host topologically nontrivial states as excellent two-dimensional topological materials. Herein, we experimentally demonstrated for the first time that the epitaxially grown high-quality antimonene monolayer islands with buckled configurations exhibit significantly robust one-dimensional topological edge states above the Fermi level. We further demonstrated that these topologically nontrivial edge states arise from a single p orbital manifold as a general consequence of atomic spin-orbit coupling. Thus, our findings establish monolayer antimonene as a new class of topological monolayer materials hosting the topological edge states for future low-power electronic nanodevices and quantum computations. KEYWORDS: Antimonene monolayer, topological edge state, quantum spin Hall effect, STM, DFT

The quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states in two-dimensional (2D) quantum materials, are intriguing emergent states characterized by a nontrivial band topology and topologically protected one-dimensional (1D) metallic edge states, which are useful for realizing novel quasi-particles such as magnetic monopoles and Majorana fermions. These quasi-particles hold promise as cores for future low-energy, high-efficiency quantum computations.1, 2 Although the most studied 2D QSH system is graphene, its electronic bandgap is extremely small, which is experimentally accessible only at extremely low temperatures.3 Therefore, various 2D topological materials with larger bandgaps have recently been theoretically proposed and experimentally investigated.4-13 Because of their strong spin-orbit coupling (SOC) and larger bandgap, the 1D topological edge states (TES) and other properties of the group-VA elemental materials such as bismuthene,14-18 phosphorene,19,

20

and antimonene

5, 9, 21-32

have been widely studied. However,

most reported experimental evidences pertain to multilayer thickness28 and flat configurations,12, 16 rather than the intrinsically buckled configuration of the monolayer films. Furthermore, while several studies have reported to obtain monolayer antimonene,33-35 no compelling support of the TES has been reported until now. Herein, we investigated the 1D TES in buckled antimonene monolayer (BAM): we fabricated a high-quality monolayer antimonene by molecular beam epitaxy (MBE) and measured the atomic and electronic structures by combining scanning tunneling microscopy/spectroscopy (STM/STS),

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low-energy electron diffraction (LEED), and X-ray photoelectron spectroscopy (XPS). Using the first-principles calculations, we demonstrated that the 1D TES originate from the band inversion of the single p orbital manifold above the Fermi level. Furthermore, the 1D TES along the rim of the antimonene nanoislands were clearly observed for the first time, using STM/STS, which are in agreement with calculations. Structural characterization of BAM. The BAM sample was fabricated by epitaxial growth on Cu(111) at the substrate temperature of 413 K and was characterized by STM/STS after cooling down to 4 K. The STM topographic images and atomic model of the antimonene sample are shown in Figures 1a-d. The first layer of antimonene on Cu(111) has a buckled structure with two sublayers (also see Figure S1), which is the same as the incipient structure in its bulk material. This rhombohedral modification (also termed as the β-form) is usually known as gray antimony.9 To investigate the edge electronic states, the antimonene islands were further fabricated on the first layer, which act as a buffer layer to screen the influence of the metal substrate on the edge electronic states of antimonene islands. The clear edge configuration of the antimonene islands is shown in Figure 1b. Figure 1c shows the large scale STM topographic image, in which both the first antimonene monolayer and the second layer (antimonene nanoislands) are visible. These islands prefer to have hexagonal shapes due to the interaction with the first BAM. Besides, some irregular edges are probably caused by defects in the substrate during the growing process. The size of these nanoislands varies from a few nanometers to more than dozens of nanometers. A high-resolution STM topography of the first buckled layer (left) and the island (right) present the same lattice, as shown in Figure 1d. The measured lattice constant of the BAM is 4.43 Å (Figure 1e), which is exactly

3 times that (2.56 Å) of the underlying Cu(111) surface. A high-resolution STM

topography further distinguishes both the sublayer antimony atoms (Figures S1a-b), confirming the buckled honeycomb structure of the BAM. The geometrical features of the antimonene film can also be verified by the sharp LEED pattern shown in Figure 1f, which reveals a uniform antimonene film. Six new hexagonal diffraction spots, circled by the orange dashed lines, are visible, showing a Cu(111)-( 3 × 3)R30º superstructure with respect to the substrate lattice (circled by a white dashed line) as well. The lattice constant (4.43 Å) of this superstructure is similar to that of crystalline bulk antimony (~4.29 Å),21 and much smaller than that of the flat antimonene (~5.01 Å).33 The formation of antimonene can be reconfirmed by the XPS spectrum shown in Figure 1g, wherein, two intrinsic 4d core peaks at

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33.15 eV and 31.59 eV are visible, which are similar to the peaks of the antimony crystal previously reported.33 The intrinsic 4d core peaks for BAM (Figure 1g) and 2p core peaks for Cu (Figure S2a) in the spectra also suggest an imperceptible chemical interaction between Sb and Cu, which is consistent with the calculated electron localization function (ELF) that demonstrates the high localization of the electrons in the Sb-Sb pairs (Figure S1c). Electronic structures of freestanding and supported antimonene monolayers. Figure 2a shows the band structure of the freestanding BAM of lattice constant 4.43 Å, with (red curves) and without (blue curves) SOC. For clarity, only the conduction bands are shown in the figure. We observe band anticrossing around 1.5 eV from the single Sb p orbital manifold, indicating topological band inversion. In order to understand the topological band inversion, the topological invariant Z2 of the freestanding BAM with inversion symmetry was calculated from the parities of the Bloch wave functions using the Fu-Kane formula, which is defined as: ( ―1)𝑍2 = ∏𝑖𝛿𝑖, where 𝛿𝑖 = ∏𝑁

𝜉 (𝑇 ) 𝑚 = 1 2𝑚 𝑖

for 2N bands of interest.36 While Z2 = 1 indicates the presence of the topologically

nontrivial edge state, Z2 = 0 indicates the trivial state. The calculated parities of the time-reversal-invariant momentum 𝑇𝑖 and the related bands are shown in Figure S3. We observe that Z2 = 0 for the first valence band (denoted as VB1 in the order of decreasing energy), and Z2 = 1 for the first conduction band (denoted as CB1 in the order of increasing energy). This indicates that there is no topologically nontrivial edge state connecting VB1 and CB1 around the Fermi level. However, a topological edge state is observed between CB1 and the second conduction band (CB2). Specifically, the 1D topological edge state of the BAM nanoribbon is plotted in Figure 2b showing the TES with a crossing Dirac point above the Fermi level. The character of splitting TES is shown in a magnified image within the energy range of [1.4, 2.0] eV (Figure 2c). The topologically nontrivial nature of the freestanding BAM can be further evidenced by calculating the evolution of the Wannier charge center (WCC) (Figure S7). Similar as above, the momentum integral is summed over CB1 in the entire Brillouin zone. We observed that the integrals of WCC over VB1 and CB1 cross the reference lines even and odd times, respectively, which agrees well with the above calculation results of the Z2 invariant. The electronic band structures of the BAM become slightly different when we consider the Cu(111) substrate (Figure 2d). Obviously, the BAM on the underlying Cu(111) substrate has the broken inversion symmetry and entangled band structures. The topological Dirac cone of the

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BAM lifted by the potential gradient of the underlying substrate consists of two spin nondegenerate branches of conduction bands that shift by ± ∆𝑘 off the Γ point, which is known as the Rashba effect (Figure 2d). The Rashba coefficient defined as αR =

2∆𝐸 ∆𝑘

is 0.90 eV·Å and

0.49 eV·Å for CB3 and CB2, respectively. These Rashba coefficients of the BAM on the three-layer Cu(111) substrate are much larger than those of prototypical semiconductor heterostructures,37-39 and the widely studied transition metal Shockley surfaces states,40,

41

but

smaller than the structures with very strong atomic SOC (e.g., bulk BiTeI with αR = 3.8 eV·Å; Bi/Ag(111) with αR = 3.05 eV·Å).42-45 This Rashba effect from the single p orbital manifold originates from the in-plane px and py orbitals. The rather large Rashba coefficients indicate that the BAM on the underlying Cu(111) substrate may have potential spintronic applications. More calculations and experimental evidences are presented in Figures S4c-d. Benefitting from the topological protection, the topological invariant for CB2 remains at Z2 =1, implying the robust 1D TES of the BAM irrespective of the support from the Cu(111) substrate or not. However, the supporting substrate complicates the observation of the topological properties in the dI/dV measurements due to the immersion in the trivial bulk band and the vanishing of the van Hove singularities (Figures 2e-f). Experimental evidence of TES. To experimentally confirm the TES in BAM experimentally, we investigated the electronic properties of the BAM nanoislands, as shown in Figure 3a. The antimonene nanoislands are superimposed on the first antimonene monolayer, which plays a buffering role by significantly decreasing the interaction with the copper substrate and supports a nearly freestanding environment for the BAM, thereby providing a possibility to observe the TES (Figure S5). To directly verify the electronic structure, a series of dI/dV spectra were measured around the island, and three typical dI/dV curves are displayed in Figure 3b. At the center of the island, the dI/dV spectrum shows a peak at the 1.68 eV (green curve in Figure 3b). Contrarily, the dI/dV curves measured at the two opposite edges (blue and red curves in Figure 3c) show peaks at 1.85 eV and 1.95 eV. The positions of these three dI/dV curves are marked by the green (center), blue, and red (edges) arrows in Figure 3a, corresponding to the colors of the spectra. To investigate the spatial evolution of the electronic structure, the spatially resolved measurement along the black dashed arrow through the nanoisland (see Figure 3a) is displayed in Figures 3c and 3d, which includes a total of 35 dI/dV spectra. The black dashed arrow across the island expands to approximately 5.6 nm. The three highlight curves (#8, #18, and #30) marked by the color-coded arrows correspond to those shown in Figure 3b. The images clearly support the

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alternating appearance of the spatially localized bulk state and the edge states. Both the bulk and edge states can be observed and distinguished in the curves #10-12 and #26-28. These measurements provide direct evidence of the existence of the TES on the BAM islands, at the energy levels between the two conductance bands CB1 and CB2, as discussed above. The spatial evolution of these three states can be observed more clearly in the color-scaled plot (Figure 3d) and the height profile (Figure 3e). The bulk state is observed to extend beyond 3 nm while the two edge states are observed to spatially expand to approximately 1 nm as marked by the white dashed lines in Figure 3d. The blue and red dashed lines in this figure coincide with the spatial region of the bulk states. (More calculations and discussions about TES can be found in Figure S6.) The observation of TES around 1.9 eV provides a strong evidence for our theoretical calculations. Furthermore, we also determined the differential of the electronic structure between the opposite edges. Owing to the support from the first antimonene buckled layer, the opposite edges of the antimonene island have unequal atomic structures. Moreover, the inversion symmetry breaking induces the breakdown of the degenerate topologically protected edge states, resulting in different characteristic peaks at the opposite edges. The inequivalent edge states residing at the opposite sides of the antimonene island are similar to those reported in bismuth.15 The spatial distribution of the TES is further demonstrated by the dI/dV mappings. To distinguish the edge states from the strong bulk state at 1.68 eV, we obtained the dI/dV mappings at 1.9 eV, 2.0 eV, and 2.1 eV in Figures 4d-f, respectively. These dI/dV mappings are measured in a region covering 5.6 nm × 7.1 nm, and the STM topography is shown in Figure 4a, which is a magnified image of the pattern in Figure 3a after probable rotation for clarity. The TES are clearly observed around the nanoisland in all the three mappings. Furthermore, the intensity of the edge states is observed to decrease as the mapping energy increases and becomes far from the edge states energy at around 1.90 eV. As a substantial contrast, we also measured the dI/dV mappings at 0.8 eV and 1.6 eV. The mapping measured at 0.8 eV (Figure 4b) shows a vacant area with no significant signal around the edge of this island, indicating the vanishing of TES. While the mapping measured at 1.6 eV (Figure 4c) only shows a strong signal concentrate near the island center, which is raised from the bulk state located at 1.68 eV, with no significant signal of TES. These spatial resolved results agree well with the observations in the spectra (Figures 3b-c), which show the TES as single peaks locate at 1.85 eV and 1.95 eV.

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The spatial feature of the TES can be clearly distinguished by comparing the STM topographic image (Figure 4g) and dI/dV mapping (Figure 4h) at 2.0 eV, which are from the region marked by the green strips in Figures 4a and 4e. The edge states emerge at a symmetric position from the edges of the island, but show a significant intensity differential, which manifests the degeneration of the electronic structure between the two edges. Because of the atomic buckling, the antimonene monolayer is flexible to adapt its lattice constant with the underlying substrate.21 According to the density functional theory (DFT) calculations, its electronic structure can be manipulated by varying the lattice constant (Figure S7), which is equivalent to tuning the strain of the BAM. Interestingly, when the lattice constant is increased to 4.70 Å, which is equivalent to a tensile strain of 10%, it becomes topologically nontrivial around the Fermi level. However, the 1D TES of BAM arising from the inverted CB1 and CB2 bands is robust against an external strain of reasonable range. Compared with the totally flat configurations,12,

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the buckled atomic structure of the BAM supports an opportunity to

control the electronic structure and topological properties by varying the lattice constant of the substrate template. Moreover, benefiting from the buffering of the first antimonene monolayer, the TES of nearly freestanding BAM can be clearly observed on the BAM islands regardless of the changes in the substrate. The robust TES of the BAM above the Fermi level may provide a new perspective to the exploration of a novel QSH conductance channel for novel quantum devices. In summary, we studied the BAM and its TES through experimental measurements combined with DFT calculations, which revealed that 1D topological protected edge states at the rim of the BAM nanoislands originate from the band inversion of the single p orbital manifold. Furthermore, we experimentally observed these TES using the dI/dV spectra at the rim of the BAM islands, which are consistent with our theoretical calculations. Therefore, our work not only provides strong evidence to generate topologically nontrivial states in the BAM, but also opens a novel route for tailoring the TES by external strain of the supporting substrate.

Methods Sample preparation and STM experiments. Antimonene was fabricated on a Cu(111) substrate in an ultrahigh vacuum (UHV) chamber, with a base pressure of 6 × 10−10 mbar, equipped with standard MBE capabilities. The Cu(111) substrate was cleaned by several cycles of sputtering, followed by annealing in the UHV chamber until it yielded a distinct Cu-(1×1) diffraction spot in a LEED pattern and clean surface terraces in the STM images. Antimony atoms (Sigma, 99.999%) evaporated from a Knudsen cell were deposited onto the clean Cu(111) substrate and maintained at

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a relatively low temperature of 413 K to avoid the formation of a possible alloy phase of antimony and copper, while a lower substrate temperature like room temperature is hard to drive a formation of ordered antimonene film due to insufficient thermal diffusion of antimony atoms. After its growth, the sample was transferred to a chamber with STM equipment for measurements. The STS data are measured at 4 K and the STM topography is obtained at room temperature and 4 K. XPS measurements. The in-situ XPS measurements were performed at the Beijing Synchrotron Radiation Facility (BSRF). The samples were stored in a UHV suitcase for transfer among different experimental stations. The photon energy of the synchrotron radiation monochromated light emitted by four high-resolution gratings, and controlled by a hemispherical energy analyzer, ranges from 10 eV to 1100 eV at an energy resolution of 0.3 eV. The photon energy of the XPS experiments was 1040 eV for Cu 2p and 180 eV for Sb 4d measurements. Calculation method. First-principles calculations within the framework of the DFT were carried out using the Vienna Ab initio simulation package (VASP), together with the projector augmented-wave method46 and Perdew–Burke–Ernzerhof exchange-correlation functional.47 The cutoff energy for the plane-wave basis was set at 400 eV and the Gamma point mesh48 of 9 × 9 × 1 for the Brillouin zone integration were employed for self-consistent calculations. The band structures of BAM and Cu(111) substrate shown in Figure 2 were investigated by placing a BAM on a three-layer slab of Cu(111)-( 3 × 3)R30 ° surface in the registry. To eliminate spurious interaction between two adjacent slabs, a vacuum layer of thickness greater than 17 Å was applied. The atomic structures of ten-layer and twenty-layer slab models used for the calculations of Rashba coefficients were relaxed until the force on each atom was less than 0.01 eV/Å and the bottom four layers of the copper atoms were fixed. The simulated STM images were obtained by calculating the local density of states in the Tersoff−Hamann approximation. The topological states associated with the geometric effect of the wave functions were calculated using Wannier9049 and WannierTools50. ASSOCIATED CONTENT Supporting Information. Atomic structure of first buckled antimonene monolayer; Z2 invariants of freestanding antimonene; Band structure, density of states and experimental dI/dV of freestanding and supported SBA; Band structures, edge states and wannier charge center φ with varying lattice constants. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION 8


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Corresponding Author * Correspondence and requests for materials should be addressed to: J.T.S. ([email protected]), Y.L.W. ([email protected]), H.J.G. ([email protected]). Author Contributions #

These authors (S.Y.Z., Y.S. and E.W.) contributed equally to this work.

ACKNOWLEDGEMENTS We acknowledge Min Ouyang and Sokrates T. Pantelides for the useful discussion. We acknowledge financial support from the National Natural Science Foundation of China (Nos. 61725107, 51572290, 61888102), National Key Research & Development Projects of China (2016YFA0202300), Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB30000000 and XDB28000000).

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(19) Zhang, J. L.; Zhao, S.; Han, C.; Wang, Z.; Zhong, S.; Sun, S.; Guo, R.; Zhou, X.; Gu, C. D.; Yuan, K. D.; Li, Z.; Chen, W. Epitaxial growth of single layer blue phosphorus: A new phase of two-dimensional phosphorus. Nano Lett. 2016, 16, (8), 4903-4908. (20) Wood, J. D.; Wells, S. A.; Jariwala, D.; Chen, K. S.; Cho, E.; Sangwan, V. K.; Liu, X.; Lauhon, L. J.; Marks, T. J.; Hersam, M. C. Effective passivation of exfoliated black phosphorus transistors against ambient degradation. Nano Lett. 2014, 14, (12), 6964-6970. (21) Chuang, F. C.; Hsu, C. H.; Chen, C. Y.; Huang, Z. Q.; Ozolins, V.; Lin, H.; Bansil, A. Tunable topological electronic structures in Sb(111) bilayers: a first-principles study. Appl. Phys. Lett. 2013, 102, (2), 022424. (22) Zhang, P.; Liu, Z.; Duan, W.; Liu, F.; Wu, J. Topological and electronic transitions in a Sb(111) nanofilm: The Interplay between quantum confinement and surface effect. Phys. Rev. B 2012, 85, (20), 1410. (23) Bian, G.; Miller, T.; Chiang, T. C. Passage from spin-polarized surface states to unpolarized quantum well states in topologically nontrivial Sb films. Phys. Rev. Lett. 2011, 107, (3), 6802. (24) Bian, G.; Wang, X.; Liu, Y.; Miller, T.; Chiang, T. C. Interfacial protection of topological surface states in ultrathin Sb films. Phys. Rev. Lett. 2012, 108, (17), 6401. (25) Ares, P.; Aguilar-Galindo, F.; Rodriguez-San-Miguel, D.; Aldave, D. A.; Diaz-Tendero, S.; Alcami, M.; Martin, F.; Gomez-Herrero, J.; Zamora, F. Mechanical isolation of highly stable Antimonene under ambient conditions. Adv. Mater. 2016, 28, (30), 6332-6336. (26) Crisostomo, C. P.; Yao, L. Z.; Huang, Z. Q.; Hsu, C. H.; Chuang, F. C.; Lin, H.; Albao, M. A.; Bansil, A. Robust large gap two-dimensional topological insulators in hydrogenated III-V buckled honeycombs. Nano Lett. 2015, 15, (10), 6568-74. (27) Ares, P.; Palacios, J. J.; Abellan, G.; Gomez-Herrero, J.; Zamora, F. Recent progress on Antimonene: A new bidimensional material. Adv. Mater. 2018, 30, (2), 1703771. (28) Kim, S. H.; Jin, K. H.; Park, J.; Kim, J. S.; Jhi, S. H.; Yeom, H. W. Topological phase transition and quantum spin Hall edge states of antimony few layers. Sci. Rep. 2016, 6, 33193. (29) Seo, J.; Roushan, P.; Beidenkopf, H.; Hor, Y. S.; Cava, R. J.; Yazdani, A. Transmission of topological surface states through surface barriers. Nature 2010, 466, (7304), 343-6. (30) Kim, S. H.; Jin, K. H.; Kho, B. W.; Park, B. G.; Liu, F.; Kim, J. S.; Yeom, H. W. Atomically Abrupt Topological p-n Junction. ACS Nano 2017, 11, (10), 9671-9677.

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(31) Fortin-Deschenes, M.; Waller, O.; Mentes, T. O.; Locatelli, A.; Mukherjee, S.; Genuzio, F.; Levesque, P. L.; Hebert, A.; Martel, R.; Moutanabbir, O. Synthesis of Antimonene on Germanium. Nano Lett. 2017, 17, (8), 4970-4975. (32) Niu, T.; Zhou, W.; Zhou, D.; Hu, X.; Zhang, S.; Zhang, K.; Zhou, M.; Fuchs, H.; Zeng, H. Modulating Epitaxial Atomic Structure of Antimonene through Interface Design. Adv. Mater. 2019, e1902606. (33) Shao, Y.; Liu, Z. L.; Cheng, C.; Wu, X.; Liu, H.; Liu, C.; Wang, J. O.; Zhu, S. Y.; Wang, Y. Q.; Shi, D. X.; Ibrahim, K.; Sun, J. T.; Wang, Y. L.; Gao, H. J. Epitaxial growth of flat antimonene monolayer: A new honeycomb analogue of graphene. Nano Lett. 2018, 18, (3), 2133-2139. (34) Wu, X.; Shao, Y.; Liu, H.; Feng, Z.; Wang, Y. L.; Sun, J. T.; Liu, C.; Wang, J. O.; Liu, Z. L.; Zhu, S. Y.; Wang, Y. Q.; Du, S. X.; Shi, Y. G.; Ibrahim, K.; Gao, H. J. Epitaxial growth and air-stability of monolayer antimonene on PdTe2. Adv. Mater. 2017, 29, 1605407. (35) Mao, Y. H.; Zhang, L. F.; Wang, H. L.; Shan, H.; Zhai, X. F.; Hu, Z. P.; Zhao, A. D.; Wang, B. Epitaxial growth of highly strained antimonene on Ag(111). Front. Phys. 2018, 13, (3), 138106. (36) Fu, L.; Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 2007, 76, (4), 045302. (37) Nitta, J.; Akazaki, T.; Takayanagi, H.; Enoki, T. Gate control of spin-orbit interaction in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure. Phys. Rev. Lett. 1997, 78, (7), 1335-1338. (38) Cheng, C.; Sun, J. T.; Chen, X. R.; Fu, H. X.; Meng, S. Nonlinear Rashba spin splitting in transition metal dichalcogenide monolayers. Nanoscale 2016, 8, (41), 17854-17860. (39) Huang, S. M.; Badrutdinov, A. O.; Serra, L.; Kodera, T.; Nakaoka, T.; Kumagai, N.; Arakawa, Y.; Tayurskii, D. A.; Kono, K.; Ono, K. Enhancement of Rashba coupling in vertical In0.05Ga0.95As/GaAs quantum dots. Phys. Rev. B 2011, 84, (8), 1098-0121. (40) LaShell, S.; McDougall, B. A.; Jensen, E. Spin splitting of an Au(111) surface state band observed with angle resolved photoelectron spectroscopy. Phys. Rev. Lett. 1996, 77, (16), 3419-3422. (41) Varykhalov, A.; Sanchez-Barriga, J.; Shikin, A. M.; Gudat, W.; Eberhardt, W.; Rader, O. Quantum cavity for spin due to spin-orbit interaction at a metal boundary. Phys. Rev. Lett. 2008, 101, (25), 256601.

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(42) Ast, C. R.; Henk, J.; Ernst, A.; Moreschini, L.; Falub, M. C.; Pacile, D.; Bruno, P.; Kern, K.; Grioni, M. Giant spin splitting through surface alloying. Phys. Rev. Lett. 2007, 98, (18), 186807. (43) Ishizaka, K.; Bahramy, M. S.; Murakawa, H.; Sakano, M.; Shimojima, T.; Sonobe, T.; Koizumi, K.; Shin, S.; Miyahara, H.; Kimura, A.; Miyamoto, K.; Okuda, T.; Namatame, H.; Taniguchi, M.; Arita, R.; Nagaosa, N.; Kobayashi, K.; Murakami, Y.; Kumai, R.; Kaneko, Y.; Onose, Y.; Tokura, Y. Giant Rashba-type spin splitting in bulk BiTeI. Nat. Mater. 2011, 10, (7), 521-6. (44) Park, J.; Jung, S. W.; Jung, M. C.; Yamane, H.; Kosugi, N.; Yeom, H. W. Self-assembled nanowires with giant Rashba split bands. Phys. Rev. Lett. 2013, 110, (3), 036801. (45) Wang, Z. F.; Yao, M. Y.; Ming, W.; Miao, L.; Zhu, F.; Liu, C.; Gao, C. L.; Qian, D.; Jia, J. F.; Liu, F. Creation of helical Dirac fermions by interfacing two gapped systems of ordinary fermions. Nat. Commun. 2013, 4, 1384. (46) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, (24), 17953-17979. (47) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, (18), 3865-3868. (48) Monkhorst, H. J.; Pack, J. D. Special points for brillouin-zone integrations. Phys. Rev. B 1976, 13, (12), 5188-5192. (49) Mostofi, A. A.; Yates, J. R.; Pizzi, G.; Lee, Y.-S.; Souza, I.; Vanderbilt, D.; Marzari, N. An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 2014, 185, (8), 2309-2310. (50) Wu, Q.; Zhang, S.; Song, H.-F.; Troyer, M.; Soluyanov, A. A. WannierTools: An open-source software package for novel topological materials. Comput. Phys. Commun. 2018, 224, 405-416.

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Figures and captions

Figure 1. Structural characterization of buckled antimonene monolayer (BAM). (a) The structural model of the BAM (orange) and antimonene nanoisland (blue) on Cu(111) substrate. (b) Side view of panel a. (c) Large-scale STM topography of the antimonene monolayer on Cu(111). (d) The atomic resolution of STM topography on the first buckled layer (left panel) and island (right panel). (e) The line profile along the black dashed line indicated in panel d, showing a lattice periodicity of 4.43 Å. (f) Sharp LEED pattern of antimonene on Cu(111), presenting a Cu(111)-( 3× 3)R30 °superstructure in the whole region. The LEED image is measured at the energy of 60 eV. (g) XPS spectrum of antimonene on Cu(111), showing two intrinsic 4d core levels of antimony.

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Figure 2. Electronic structures of freestanding and supported antimonene monolayers. (a) Band structure for freestanding BAM with (red curves) and without (blue curves) SOC. Band anticrossing is observed between CB1 and CB2 in the presence of SOC. (b) The band structure spectra for the semi-infinite freestanding BAM nanoribbon obtained via constructing the effective Hamiltonian of the maximally localized Wannier function. (c) A magnified image of panel b, as marked in the red box in panel b showing two nondegenerate edge states. (d) The projected band structure of BAM on the Cu(111) surface. Only three layers of the Cu(111) slab have been used for better visualization. The gray curves and red dots are weighted by the Cu(111) substrate and BAM, respectively. (e) Band structure of the semi-infinite BAM nanoribbon supported on Cu(111). (f) A magnified image of panel e, as marked in the red box. (b, c, e, f) are obtained via constructing the effective Hamiltonian of the maximally localized Wannier function.

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Figure 3. Experimental evidence for topological edge states. (a) STM topography of a representative antimonene island with an irregular hexagonal shape. (b) Three dI/dV curves measured at the edges and center of the nanoisland, which are marked by blue, green, and red arrows in panel a. (c) A waterfall-like plot of a spatially resolved measurement, which consists of 35 dI/dV curves along the black dashed arrow in panel a. The indexes of these curves are marked on the left. The three dI/dV curves marked by arrows correspond to those shown in c, with peaks at 1.68 eV (red), 1.85 eV (blue), and 1.95 eV (green). (d) The intensity plot of the spatially resolved measurement shown in panel d. (e) A line profile across the black dashed arrow in panel a, which expanded to 5.6 nm. The y-axis corresponds to that in panel d.

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Figure 4. Spatial distribution of topological edge states. (a) Magnified topography of Figure 3a, covering a range of 5.6 nm × 7.1 nm. (b-c) The dI/dV mapping at 0.8 eV and 1.6 eV, respectively, showing no feature of topological edge states. The mapping measured at 1.6 eV shows a strong signal of the bulk state, which is located at 1.68 eV. (d-f) The dI/dV mapping at 1.9 eV, 2.0 eV, and 2.1 eV, respectively. The clear feature of topological edge states around the nanoisland show substantial contrast with that shown in panels b-c, which agree well with the behavior shown in Figures 3b-d. (g) The three-dimensional vision of the island topography, showing a magnified region ranging 5.6 nm × 2.0 nm marked by the green strip in panel a. (h) The three-dimensional view of dI/dV mapping of the island, showing the region marked by green strip in panel e, corresponding to the region in panel a. The color-code arrows agree with those in Figure 3a.

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For TOC only

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Evidence of Topological Edge States in Buckled Antimonene

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