Two-Dimensional In–Sb Compound on Silicon as ... - ACS Publications

Letter Cite This: Nano Lett. 2018, 18, 4338−4345

pubs.acs.org/NanoLett

Two-Dimensional In−Sb Compound on Silicon as a Quantum Spin Hall Insulator Dimitry V. Gruznev,† Sergey V. Eremeev,‡,¶ Leonid V. Bondarenko,† Alexandra Yu. Tupchaya,† Alexey A. Yakovlev,† Alexey N. Mihalyuk,†,§ Jyh-Pin Chou,∥ Andrey V. Zotov,†,§ and Alexander A. Saranin*,†,§ †

Institute of Automation and Control Processes FEB RAS, 690041 Vladivostok, Russia Institute of Strength Physics and Materials Science SB RAS, Tomsk 634055, Russia ¶ Tomsk State University, Tomsk 634050, Russia § School of Natural Sciences, Far Eastern Federal University, 690950 Vladivostok, Russia ∥ Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong 999077, China

Nano Lett. 2018.18:4338-4345. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 09/12/18. For personal use only.

‡

ABSTRACT: Two-dimensional (2D) topological insulator is a promising quantum phase for achieving dissipationless transport due to the robustness of the gapless edge states resided in the insulating gap providing realization of the quantum spin Hall effect. Searching for two-dimensional realistic materials that are able to provide the quantum spin Hall effect and possessing the feasibility of their experimental preparation is a growing field. Here we report on the twodimensional (In, Sb)2 3 ×2 3 compound synthesized on Si(111) substrate and its comprehensive experimental and theoretical investigations based on an atomic-scale characterization by using scanning tunneling microscopy and angle-resolved photoelectron spectroscopy as well as ab initio density functional theory calculations identifying the synthesized 2D compound as a suitable system for realization of the quantum spin Hall effect without additional functionalization like chemical adsorption, applying strain, or gating. KEYWORDS: Electronic properties and materials, quantum spin Hall effect, surfaces, interfaces and thin films, ARPES, STM, DFT

D

that in the case of a 2D semimetal with a honeycomb-like structure (such as graphene) any finite SOC will lift the band degeneracy and open a nontrivial SOC gap to turn the system into a QSH insulator. In the second model introduced by Bernevig, Hughes, and Zhang (BHZ model),6 the SOC affects the band structure of a narrow-band semiconductor in a way that the trivial band gap closes and the nontrivial band opens, accompanied by a band inversion between the valence and conduction bands. However, the fast progress on the theoretical front has been much slower in the experimental synthesis of QSH insulators.1 One of the challenging problems is a proper choice of a suitable substrate where the QSH insulator film can be safely grown or placed. Bi bilayers on Bi2Te38 and Bi2Te2Se,9 bismuthene on SiC(0001),7 and FeSe on SrTiO3(001)10 are among seldom positive results. Single-crystalline silicon, the most widely used semiconductor material, seems to be one of the most desirable substrates, and QSH insulators might be found among the so-called adsorbate-induced silicon reconstructions (i.e., ordered monolayer and submonolayer films of

iscovery of the topological insulators (TIs) is believed to be one of the most seminal breakthroughs in modern condensed-matter physics. Topological insulator is a material in which a sufficiently strong spin−orbit coupling (SOC) inverts its bulk band gap, which distinguishes them from a trivial insulator that has no band inversion. The most fascinating consequence of the band inversion is the occurrence of the topologically protected metallic surface or edge states (for three- (3D) and two-dimensional (2D) TIs, respectively) with helical spin polarization inside an insulating bulk band. The remarkable feature of these states is negligible elastic electron scattering that, in principle, allows achieving dissipationless spin current for future spintronic and quantum computing devices utilizing these materials. A number of 3D TIs have been synthesized experimentally (e.g., with various dichalcogenides). However, 2D TIs, also known as quantum spin Hall (QSH) insulators,1−4 are considered to have an advantage over their 3D counterparts in view of a more robustness of the edge states against backscattering since there the only available backscattering channel is forbidden. Hence, the search for the 2D materials having properties of the QSH insulator presents an urgent challenge for the researches. The search field was delineated theoretically by the two seminal models. In the first model, introduced by Kane and Mele (KM model),5 it is suggested © 2018 American Chemical Society

Received: April 3, 2018 Revised: June 14, 2018 Published: June 21, 2018 4338

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345

Letter

Nano Letters

Figure 1. Room-temperature (RT) (a) 50 × 50 nm2 and (b) 10 × 10 nm2 STM images, and (c) LEED pattern (54 eV) of the (In, Sb)/Si(111) surface. Small and large arrows in panel (a) indicate two typical types of the surface defects (see the text). Inset in (a) shows close-up STM image of the outlined area and illustrates occurrence of the two mirror domains with opposite orientations of the trimer-like features. Low-temperature (LT) (d) 50 × 50 nm2 and (e) 10 × 10 nm2 STM images and (f) LEED pattern (54 eV) of the (In, Sb)/Si(111) surface. The ordered 2 3 ×2 3 arrays (outlined by a dashed line in panel (d)) are indicated by character A in panels (d) and (e) and regions with lacking the long-range order are indicated by character B. The dashed rhombus in panels (b) and (e) outline the 2 × 2 and 2 3 ×2 3 unit cells, respectively. The main reflections in the LEED patterns are outlined by blue circles to guide the eye.

a distorted In−Sb bilayer having 2 × 2 periodicity and In trimers arranged into a 2 3 ×2 3 honeycomb structure atop the bilayer. The most important feature of the electron band structure of the (In, Sb)/Si(111) 2D compound is an occurrence of the nontrivial gap at the Fermi level. The 2D In−Sb compound can be fabricated on Si(111) using room temperature (RT) deposition of Sb onto the preformed In/Si(111) surfaces followed by annealing at about 500 °C.32,33 The In/Si(111) surfaces might be either the quasihexagonal hex- 7 × 3 or quasi-rectangular rec- 7 × 3 reconstructions with nominal In coverages of 1.2 and 2.4 ML, respectively,34 or their mixture. The formation procedure appears to be essentially insensitive to initial In coverage since upon annealing above ∼500 °C any excess of In atoms desorbs from the surface. In contrast, the amount of Sb is crucial, and it has not exceeded ∼0.75 ML. If Sb coverage approaches 1.0 ML, which is enough for the formation of the pristine Sb reconstructions, Sb/Si(111) 3 × 3 or Sb/Si(111)2 × 1, the binary In−Sb layer disintegrates leaving the more stable Sb/Si(111) reconstructions on the surface. In room-temperature scanning tunneling microscopy (STM) images (Figure 1a,b), the 2D In−Sb compound shows up the 2 × 2-periodic hexagonal structure built of trimer-like features, and this structure occurs in two possible orientations. Two types of unavoidable defects present in the interior of 2 × 2 domains, namely, single trimer vacancies and larger pits of irregular shape (indicated by small and large arrows, respectively). Both types of defects are due to local coverage fluctuations; we attribute the former defects to a local deficit of

adsorbates on silicon). They have already proved to be advanced 2D materials with fascinating properties (e.g., they can exhibit giant Rashba effect,11−14 be the world’s thinnest superconductors,15−18 or merge together giant Rashba effect and superconductivity19). Finding the QSH insulator among the silicon reconstructions would be a dignified extension of this list. Possibility for growing QSH insulators on silicon, namely, Si(111) surface, has been predicted theoretically in numerous works (e.g., refs 20−27). Except for a few exclusions (e.g., refs 25−27), the main approach follows directly the idea of the KM model and resides in a simple placing of the buckled honeycomb bilayers of various chemical compositions atop the bulk-like terminated Si(111) surface. From the viewpoint of experimentalists, these studies look like theoretical exercises with toy models. Indeed, none of the predicted structures have been synthesized. In reality, adsorbates on Si(111) selfassemble typically into the 2D structures very different from the simple honeycomb-like bilayers.28,29 The breakthrough has been made by Zhang et al.30 who basing on the structural model of the recently synthesized 2D (Bi, Ag)-4 × 4 compound on Si(111)31 concluded that the compound possesses the properties of the QSH material. In the present Letter, we report on the discovery of a new QSH insulator among 2D compounds on silicon. This is the 2D (In, Sb)-2 3 ×2 3 compound formed on Si(111) surface by 1.25 ML of In and 0.75 ML of Sb [1 ML (monolayer) = 7.8 × 1014 cm−2, top Si atom density of unreconstructed Si(111) surface]. Its atomic structure can be visualized as consisting of 4339

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345

Letter

Nano Letters

Figure 2. Structural models (top and side views) of the 2 3 ×2 3 structure (left panel), 2 × 2 structure (middle panel), and the distorted In−Sb bilayer from which the In trimers were removed (right panel). Corresponding unit cells are outlined by the dashed rhombuses. Sb atoms are shown by gray circles and In atoms by red circles. The brighter color and larger circles are for the higher-located atoms. Si atoms are shown by small blue circles (T1 site), yellow circles (T4 site), and white circles (second Si bilayer). Irregular hexagons hatched by different colors, green, blue, and violet, in the right panel constitute the structure of the In−Sb bilayer.

started with the 2 × 2 structure which the optimized model is shown in the middle part of Figure 2. The 2 3 ×2 3 structural model shown in the left panel in Figure 2 is obtained from the 2 × 2 model just by removing every third In trimer with subsequent structure relaxation. Change of the 2 × 2 structure for the 2 3 ×2 3 one results in a change of the compressive surface stress of −797 meV/Å2 for the tensile stress of +68 meV/Å2 and a decrease of the structure formation energy by 96 meV per 1 × 1 unit cell. The very top layer of the (In, Sb)/Si(111)2 3 ×2 3 structure contains 0.5 ML of In, which forms In trimers arranged into the 2 3 ×2 3 -periodic honeycomb structure. The two In trimers constituting the 2 3 ×2 3 unit cell are slightly different in size, having In−In bond lengths of 3.42 and 3.38 Å. The trimers reside on the distorted buckled In−Sb bilayer containing 0.75 ML of In and 0.75 ML of Sb. The right side of Figure 2 illustrates the atomic arrangement of the In− Sb bilayer. One can see that In atoms reside close to the T1 (on-top) sites, while Sb atoms occupy H3, T4, and T1 sites. Sb atoms in H3 and T4 sites reside 1.8 Å higher than Sb atoms in T1 sites. The top In trimers are centered above Sb atoms in the T1 site. Arrangement of the In−Sb bilayer can be visualized as stacking of the irregular hexagons of three types (hatched by different colors in Figure 2) differing by their orientations due to rotation by 120°. As clearly seen in the side view of the model in Figure 2, the structure can also be considered as consisting of the upper In− Sb layer composed of In trimers (0.5 ML) and topmost Sb atoms (0.5 ML) and the lower flat In−Sb layer with 0.75 ML of In and 0.25 ML of Sb. Such kind of description appears to be more convenient for further analysis of the electronic properties. To check the validity of the proposed structural model, we have used it to simulate STM images and to compare them with their experimental counterparts, as well as to calculate the electron band structure and to compare it with the ARPES

In (as will be shown below) and the latter to a local increase in Sb coverage resulting in the formation of small 3 × 3 -Sb patches. Nevertheless, almost the entire surface is covered with the well-ordered 2 × 2 structure and displays a sharp and bright 2 × 2 LEED pattern (Figure 1c). When the In−Sb layer is cooled down to low temperatures (LT) of ∼110 K or below, its STM appearance changes due to “disappearance” of certain portion of trimers. Ordering of the trimer vacancies results in the arrays with a honeycomb 2 3 ×2 3 structure (indicated by character A in Figure 1d,e). However, disappearance of two or more neighboring trimers (that often occurs in the vicinity of surface defects and domain boundaries) results in the loss of the long-range order (arrays indicated by character B in Figure 1d,e). However, the ordered 2 3 ×2 3 arrays are large and common enough to yield the 2 3 -order reflections in the LEED pattern (Figure 1f). STM observations at intermediate temperature of ∼170 K (not shown) provide a hint for understanding the origin of the difference between RT- and LT-STM appearance of the (In, Sb)/Si(111) surface. At this temperature, the STM features looks fuzzy, as occupied and vacant trimer sites change dynamically during recording STM images. This can serve as an indication of the hopping motion of the adsorbate atoms. Thus, one can conclude that the RT-STM images show a timeaveraged pattern where almost all 2 × 2 trimer sites are seen as occupied. The LT-STM images display a pattern when any dynamic motion of adsorbates is frozen. To establish a structural model of the (In, Sb)/Si(111) surface, we have applied the ab initio random structure searching (AIRSS) technique.35 In the AIRSS calculations, less rigorous requirements have been employed than those used at the stage of refining the final structure, namely, the number of Si bilayers in the slab has been reduced to two, SOC was not taken into account, and the considered structures have been limited to only those having C3 symmetry, while all other calculation parameters (e.g., number of k-points, cutoff energy, the level of residual force) have been preserved. We have 4340

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345

Letter

Nano Letters

Figure 3. Resemblance of the (In, Sb)/Si(111)2 3 ×2 3 model to the experimental data. (a,b) Simulated and (d,e) experimental STM images. (c) Calculated band structure of the 2 3 ×2 3 model obtained using band unfolding technique and (f) experimental ARPES spectrum.

perpendicular to the wavenumber (positive and negative, respectively) that are localized at the (In, Sb) adlayer. In contrast to other binary 2D phases on semiconductor substrates like (Tl, Bi),28 (Au, Al),38 (Tl, Sn),39 and (Tl, Pb),40 which have spectra possessing the Rashba splitting with metallic character, the spectrum of the (In, Sb)/Si(111)2 3 ×2 3 along with Rashba splitting in the 2D bands demonstrates a gap of 25 meV at the Fermi level near the Γ point (see green rectangle in Figure 4a) wherein the gap at Γ amounts to 127.5 meV. Considering the orbital composition of the bands near the Fermi level (Figure 4b), we found that at large k∥ the occupied band is primarily composed by pxy orbitals of the topmost Sb atoms and that the unoccupied one is determined by pxy orbitals of In atoms forming trimers. The pz contribution is smaller (see Figure 4c) and it comes mostly from the lower flat In−Sb layer atoms. However, in the vicinity of Γ the orbital order is inverted, indicating nontrivial topology of the system. To determine whether the gap is determined by the spin−orbit interaction, we have performed the calculations varying the SOC constant λ from its natural value, λ0, to zero. It has been found that both the Rashba splitting and the Γ gap decrease with reducing the λ, and at λ/λ0 = 0.14, the gap gets closed (Figure 4d−g). At λ = 0, i.e., with switched off spin−orbit coupling, the spectrum is gapped again with the gapwidth of 18 meV and normal (uninverted) band order at the Γ point (Figure 4h). Transition through a zero gap at the variation of the λ/λ0 indicates the SOC-induced nontrivial topology of the 2D (In, Sb) system. As can be seen in Figure 4i, the SOCinduced Γ gap demonstrates typical linear dependence on the SOC strength, whereas the absolute gap, determined by the orbital hybridization, is almost insensitive to the λ variation in the topological phase in the range of λ/λ0 = [0.5−1]. It is noteworthy that the QSH phase is provided by the coupling of the 2D In−Sb film to silicon substrate, and it is stable with decreasing Si(111) thickness down to a single Si bilayer (Figure 5a). As can be seen, the surface spectrum demonstrates the same inverted gap at the Fermi level. The nontrivial topological character of the (In, Sb)/Si(111)-

data. The results of comparison are presented in Figure 3. In particular, Figure 3a,b;d,e show simulated and experimental dual-bias (±1.0 V) STM images, respectively. One can see a perfect coincidence including very fine features, e.g., the slight size difference between the two trimers constituting the 2 3 ×2 3 unit cell in the filled-state images. Figure 3f shows the ARPES spectrum from the (In, Sb)/Si(111) surface acquired at 78 K. Remember that this surface resembles a mixture of the ordered 2 3 ×2 3 regions and areas without long-range order (Figure 1d). This seems to be a reason that the ARPES spectrum follows a basic 2 × 2 periodicity. In order to compare the calculated band structure (which is shown in Figure 4 and will be discussed in detail later) with the experimental ARPES data, we have applied to the former a band unfolding technique,36,37 whose result is shown in Figure 3c. One can see that this calculated spectrum demonstrates a clear resemblance with the experimental ARPES spectrum. The coincidence is especially proper for Γ and M points, while some week spectral features available in the K point in the 2 × 2 unfolded spectrum are poorly resolved in the ARPES spectrum. In the calculated band structure, the bands in the vicinity of K point might be replicas of bands around Γ point appearing as a consequence of the unfolding procedure since the K point in the 2 × 2 SBZ coincides with the Γ1 point in the 2 3 ×2 3 SBZ. As such they are not visible in the experimental spectrum. Thus, one can see that simulated and experimental STM images demonstrate a close resemblance and that there is a reasonable coincidence between experimental ARPES data and calculated spectrum obtained using the unfolding technique. All these together can serve an argument for the validity of the proposed structural model of the (In, Sb)/Si(111)2 3 ×2 3 surface. By obtaining a proper structural model, we have got a possibility to explore electronic properties of the 2 3 ×2 3 ordered In−Sb 2D phase. The spin-resolved band structure of the (In, Sb)/Si(111) calculated within 2 3 ×2 3 SBZ is shown in Figure 4a. The red and blue points in Figure 4a correspond to the states with in-plane spin polarization 4341

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345

Letter

Nano Letters

Figure 4. (a) Electronic spectrum of the (In, Sb)/Si(111) calculated within 2 3 ×2 3 SBZ. (b,c) Magnified view of the area bordered by a green rectangle in panel (a) with marked In and Sb orbitals, pxy and pz, respectively. (d−h) Behavior of the spectrum at decreasing spin−orbit coupling strength up to its zero value. (i) Dependence of the Γ and absolute gaps on the SOC strength; positive (negative) sign of the gap corresponds to the trivial insulator (topological insulator) phase.

the contrary, the spectrum of the free-standing In−Sb film is strongly metallic with a trivial gap at 0.8−1.0 eV above the Fermi level (Figure 5c). Such a behavior is related to complicated charge redistribution between the upper In−Sb layer, lower flat In−Sb layer, and Si substrate. In the upper In− Sb layer, In atoms forming trimers give away ∼1/3 electrons as compared to the charge of the neutral atom, while the Sb atoms accept about 0.4−0.5 electrons. As a result, the upper In−Sb layer has an extra charge of 1.1 electrons, and the lower flat In−Sb layer composed of nine In atoms and three Sb atoms lost ∼1.8 electrons. The charge transfer in an amount of

2 3 ×2 3 system stemmed from band inversion between the pxy orbitals of the upper In−Sb layer composed of In trimers and the topmost Sb atoms can also be verified by calculation of the 2 topological invariant. It was calculated by using the method based on tracking the evolution of hybrid Wannier charge centers (WCCs) for all occupied bands as realized in Z2 Pack.41,42 The corresponding evolution of WWCs for the structure with a single Si bilayer is shown in Figure 5b. The path following the largest gap in x̅n jumps over the WCC bands an odd number of times, which yields 2 = 1 and directly confirms the QSH phase in (In, Sb)/Si(111)-2 3 ×2 3 . On 4342

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345

Letter

Nano Letters

Figure 5. (a) Electronic band structure of the (In, Sb)/Si(111) film containing one Si(111) bilayer; (b) evolution of WCCs x̅n (circles) and their largest gap midpoints (blue rhombi) vs ky for kx = 0 plane; (c) spectrum of free-standing (In, Sb)-2 3 ×2 3 .

Figure 6. (a) Atomic structure of (In, Sb)/Si(111)-2 3 ×2 3 unit cell (green rhombus) and related rectangular cell (red rectangle). We construct the cell for calculation of the edge states by repeating the rectangular cell in the x direction. (b) Part of the computational cell of (In, Sb)/Si(111) containing the groove in (In, Sb) adlayer. (c) Electronic spectrum of (In, Sb)/Si(111) obtained with In d-electrons excluded in the calculation. (d) Edge spectrum calculated along ky direction of the 1D BZ. Light blue shaded area marks projection of the 2D electronic spectrum.

∼0.7 electrons provides the bonding of the In−Sb film with the silicon substrate. Next, we consider the edge electronic structure of the (In, Sb)/Si(111) 2D TI. As expected from the effective continuous model,43 the decay depth of the topological edge states in 2D TI should be much larger than that for the Dirac surface states in 3D TI. Hence, to avoid the finite size effect when calculating the edge spectrum, the distance between neighboring edges should be chosen as large as possible. We have constructed the computational cell on the base on the rectangular cell (Figure 6a), which was increased eight times along the x direction, and then the groove of the width of about 25 Å in the (In, Sb) adlayer along the y direction was prepared (Figure 6b). In the

resulting computational cell, the distance between edges amounts to ∼160 Å. As the silicon substrate we used a single Si(111) bilayer, which, as we have shown above, is sufficient for reproducing the nontrivial band spectrum of the (In, Sb)/ Si(111)-2 3 ×2 3 system. Such computational cell contains about 1000 atoms, and in order to simplify the calculations, we excluded the In d-electrons from the treatment. It results in a five-times decrease in the Γ gap of the 2D spectrum, while the absolute gap decreases only by ∼40% and amounts to 16 meV (see yellow stripe in Figure 6c). However, it is important that such modification of the spectrum does not change its topology and that the gap remains inverted. The calculated electronic structure of the edge is shown in Figure 6d. As can 4343

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345

Letter

Nano Letters be seen in the figure, the spectrum has a gapless Dirac-like state in the 1D Brillouin zone center, stemming from the nontrivial band topology, as well as a number of almost dispersionless dangling bond states below and above the Fermi level, which are originated from the broken bonds at the groove edge. The highest occupied dangling bond state lying near the gap region is strongly hybridized with the topological Dirac state. In summary, we have succeeded in fabrication of the QSH insulator system on a silicon substrate. The atomic structure of the grown 2D In−Sb compound was successfully decrypted by STM measurements and DFT calculations as consisting of distorted In−Sb bilayer having 2 × 2 periodicity and In trimers arranged into a 2 3 ×2 3 honeycomb structure atop the bilayer. The nontrivial quantum state of the grown structure was verified by band inversion analysis and 2 invariant calculation. It was shown that nontrivial topology is originated from pxy band inversion of the upper In−Sb layer. The effect of the substrate on the topological phase has also been elucidated. It was found that coupling of the In−Sb film to the Si substrate plays a crucial role in its unique electronic band structure formation. The discovered 2D topological insulator has an inverted gap at the Fermi level, which should ensure the formation of a single pair of gapless helical edge states for realization of the QSH effect in the system without additional tuning of the chemical potential. Our findings provide a new innovative platform for design of the QSH devices on a silicon substrate. Methods. The experiments were performed in an ultrahighvacuum Omicron MULTIPROBE system (base pressure ≤ ∼2.0 × 10−10 Torr) by means of scanning tunneling microscopy (STM), low energy electron diffraction (LEED), and angle-resolved photoelectron spectroscopy (ARPES) methods. Atomically clean Si(111)7 × 7 surfaces were prepared in situ by flashing to 1280 °C after the samples were first outgassed at 600 °C for several hours. Both In and Sb were deposited from Ta boats. The Sb deposition rate was calibrated using STM observations of the formation of the Si(111) 3 × 3 -Sb phase with known saturation coverage of 1 ML. STM images were acquired using Omicron variabletemperature STM-XA operating in a constant-current mode. Mechanically cut PtIr tips were used as STM probes after annealing in vacuum. ARPES measurements were conducted using a VG Scienta R3000 electron analyzer and high-flux He discharge lamp (hν = 21.2 eV) with a toroidal-grating monochromator as a light source. Theoretical methods. Our calculations were based on DFT as implemented in the Vienna ab initio simulation package VASP44,45 using a planewave basis set. The projectoraugmented wave approach46 was used to describe the electron−ion interaction, and the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE)47 was employed as the exchange-correlation functional. The scalar relativistic effect and the spin−orbit interaction (SOI) were taken into account. To simulate the In−Sb reconstructions on Si(111), we used a slab consisting of four bilayers (BL) of silicon, at the PBE-optimized bulk Si lattice constant. Hydrogen atoms were used to passivate the Si dangling bonds at the bottom of the slab. The atomic positions of adsorbed atoms and atoms of Si layers within the three BLs of the slab were optimized. Silicon atoms of the deeper layers were kept fixed at the bulk crystalline positions. The kinetic cutoff energy was 250 eV, and a 5 × 5 × 1 k-point mesh was

used to sample the surface Brillouin zone. The geometry optimization was performed until the residual force on atoms was smaller than 10 meV/Å. Since the DFT underestimates the bulk band gap in silicon, for the band structure calculations, we applied an approximate quasi-particle approach DFT-1/2,48,49 as was described in ref 50. Topological 2 invariant was calculated by using Z2 Pack.41,42 For analysis of the results on the electronic band structure of the (In, Sb)-2 3 ×2 3 compound on Si(111), we recovered the effective primitive cell band structure through the supercell calculations by using the BandUP code.36,37 The core procedure of the unfolding band structure was to calculate a spectral function and the spectral weights derived from the plane-wave expansion coefficients of the supercell eigenstates, which can be directly compared to ARPES measurements.37

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +7 (423) 231 0426. ORCID

Sergey V. Eremeev: 0000-0002-9477-3017 Alexander A. Saranin: 0000-0001-6642-2466 Author Contributions

D.V.G., L.V.B., A.Y.T., and A.A.Y. carried out ARPES and STM experiments. A.N.M., J.P.C., and S.V.E. carried out the calculations. A.V.Z., S.V.E., D.V.G., and A.A.S. wrote the manuscript and conceived and coordinated the project. All authors contributed to the manuscript editing. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

The work was supported in part by Russian Foundation for Basic Research (Grant 17-02-00567), Russian Science Foundation (Grant 14-12-00479-P, for experimental measurements and partly for DFT calculations and Grant 18-12-00169, for theoretical investigation of the band topology), and RAS Headquater Program for Basic Research #32 (Grant 02622018-0062). The calculations were conducted using the equipment of Shared Resource Center “Far Eastern Computing Resource” IACP FEB RAS (https://cc.dvo.ru).

(1) Kou, L.; Ma, Y.; Sun, Z.; Heine, T.; Chen, C. J. Phys. Chem. Lett. 2017, 8, 1905−1919. (2) Wang, Z. F.; Jin, K. H.; Liu, F. WIREs Comput. Mol. Sci. 2017, e1304. (3) Huang, H.; Xu, Y.; Wang, J.; Duan, W. WIREs Comput. Mol. Sci. 2017, e1296. (4) Ren, Y.; Qiao, Z.; Niu, Q. Rep. Prog. Phys. 2016, 79, 066501. (5) Kane, C. L.; Mele, E. J. Phys. Rev. Lett. 2005, 95, 226801. (6) Bernevig, B. A.; Hughes, T. L.; Zhang, S. C. Science 2006, 314, 1757−1761. (7) Reis, F.; Li, G.; Dudy, L.; Bauernfeind, M.; Glass, S.; Hanke, W.; Thomale, R.; Schäfer, J.; Claessen, R. Science 2017, 357, 287−290. (8) Yang, F.; Miao, L.; Wang, Z. F.; Yao, M.-Y.; Zhu, F.; Song, Y. R.; Xu, J.-P.; Fedorov, A. V.; Sun, Z.; Zhang, G. B.; Liu, C.; Liu, F.; Qian, D.; Gao, C.; Jia, J.-F. Phys. Rev. Lett. 2012, 109, 016801. (9) Kim, S. H.; Jin, K.-H.; Park, J.; Kim, J. S.; Jhi, S.-H.; Kim, T.-H.; Yeom, H. W. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 155436. 4344

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345

Letter

Nano Letters

(36) Medeiros, P. V. C.; Stafström, S.; Björk, J. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 041407. (37) Medeiros, P. V. C.; Tsirkin, S. S.; Stafström, S.; Björk, J. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 041116. (38) Gruznev, D. V.; Bondarenko, L. V.; Matetskiy, A. V.; Tupchaya, A. Y.; Chukurov, E. N.; Hsing, C. R.; Wei, C. M.; Eremeev, S. V.; Zotov, A. V.; Saranin, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 245407. (39) Gruznev, D. V.; Bondarenko, L. V.; Matetskiy, A. V.; Tupchaya, A. Y.; Alekseev, A. A.; Hsing, C. R.; Wei, C. M.; Eremeev, S. V.; Zotov, A. V.; Saranin, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 035421. (40) Gruznev, D. V.; Bondarenko, L. V.; Matetskiy, A. V.; Yakovlev, A. A.; Tupchaya, A. Y.; Eremeev, S. V.; Chulkov, E. V.; Chou, J. P.; Wei, C. M.; Lai, M. Y.; Wang, Y. L.; Zotov, A. V.; Saranin, A. A.; et al. Sci. Rep. 2015, 4, 4742. (41) Soluyanov, A. A.; Vanderbilt, D. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 235401. (42) Gresch, D.; Autès, G.; Yazyev, O. V.; Troyer, M.; Vanderbilt, D.; Bernevig, B. A.; Soluyanov, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 95, 075146. (43) Linder, J.; Yokoyama, T.; Sudbø, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 205401. (44) Kresse, G.; Hafner, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558. (45) Kresse, G.; Joubert, D. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758. (46) Blöchl, P. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (47) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (48) Ferreira, L. G.; Marques, M.; Teles, L. K. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 125116. (49) Ferreira, L. G.; Marques, M.; Teles, L. K. AIP Adv. 2011, 1, 032119. (50) Matetskiy, A. V.; Kibirev, I. A.; Mihalyuk, A. N.; Eremeev, S. V.; Gruznev, D. V.; Bondarenko, L. V.; Tupchaya, A. Y.; Zotov, A. V.; Saranin, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96, 085409.

(10) Wang, Z. F.; Zhang, H.; Liu, D.; Liu, C.; Tang, C.; Song, C.; Zhong, Y.; Peng, J.; Li, F.; Nie, C.; Wang, L.; Zhou, X. J.; Ma, X.; Xue, Q. K.; Liu, F. Nat. Mater. 2016, 15, 968. (11) Gierz, I.; Suzuki, T.; Frantzeskakis, E.; Pons, S.; Ostanin, S.; Ernst, A.; Henk, J.; Grioni, M.; Kern, K.; Ast, C. R. Phys. Rev. Lett. 2009, 103, 046803. (12) Sakamoto, K.; Kakuta, H.; Sugawara, K.; Miyamoto, K.; Kimura, A.; Kuzumaki, T.; Ueno, N.; Annese, E.; Fujii, J.; Kodama, A.; Shishidou, T.; Namatame, H.; Taniguchi, M.; Sato, T.; Takahashi, T.; Oguchi, T. Phys. Rev. Lett. 2009, 103, 156801. (13) Sakamoto, K.; Oda, T.; Kimura, A.; Miyamoto, K.; Tsujikawa, M.; Imai, A.; Ueno, N.; Namatame, H.; Taniguchi, M.; Eriksson, P. E. J.; Uhrberg, R. I. G. Phys. Rev. Lett. 2009, 102, 096805. (14) Sakamoto, K.; Kim, T. H.; Kuzumaki, T.; Mü ller, B.; Yamamoto, Y.; Ohtaka, M.; Osiecki, J. R.; Miyamoto, K.; Takeici, Y.; Harasawa, A.; Stolwijk, S. D.; Schmidt, A. B.; Fujii, J.; Uhrberg, R. I. G.; Donath, M.; Yeom, H. W.; Oda, T.; et al. Nat. Commun. 2013, 4, 2073. (15) Zhang, T.; Cheng, P.; Li, W. J.; Sun, Y. J.; Wang, G.; Zhu, X. G.; He, K.; Wang, L.; Ma, X.; Chen, X.; Wang, Y.; Liu, Y.; Lin, H. Q.; Jia, J. F.; Xue, Q. K. Nat. Phys. 2010, 6, 104−108. (16) Uchihashi, T.; Mishra, P.; Aono, M.; Nakayama, T. Phys. Rev. Lett. 2011, 107, 207001. (17) Yamada, M.; Hirahara, T.; Hasegawa, S. Phys. Rev. Lett. 2013, 110, 237001. (18) Ichinokura, S.; Bondarenko, L. V.; Tupchaya, A. Y.; Gruznev, D. V.; Zotov, A. V.; Saranin, A. A.; Hasegawa, S. 2D Mater. 2017, 4, 025020−10. (19) Matetskiy, A. V.; Ichinokura, S.; Bondarenko, L. V.; Tupchaya, A. Y.; Gruznev, D. V.; Zotov, A. V.; Saranin, A. A.; Hobara, R.; Takayama, A.; Hasegawa, S. Phys. Rev. Lett. 2015, 115, 147003. (20) Zhou, M.; Ming, W.; Liu, Z.; Wang, Z.; Li, P.; Liu, F. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 14378−14381. (21) Zhou, M.; Ming, W.; Liu, Z.; Wang, Z.; Yao, Y.; Liu, F. Sci. Rep. 2015, 4, 7102. (22) Yao, L. Z.; Crisostomo, C. P.; Yeh, C. C.; Lai, S. M.; Huang, Z. Q.; Hsu, C. H.; Chuang, F. C.; Lin, H.; Bansil, A. Sci. Rep. 2015, 5, 15463. (23) Crisostomo, C. P.; Yao, L. Z.; Huang, Z. Q.; Hsu, C. H.; Chuang, F. C.; Lin, H.; Albao, M. A.; Bansil, A. Nano Lett. 2015, 15, 6568−6574. (24) Fu, H.; Liu, Z.; Lian, C.; Zhang, J.; Li, H.; Sun, J. T.; Meng, S. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 035427. (25) Chuang, F. C.; Hsu, C. H.; Chou, H. L.; Crisostomo, C. P.; Huang, Z. Q.; Wu, S. Y.; Kuo, C. C.; Yeh, W. C. V.; Lin, H.; Bansil, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 035429. (26) Zhou, J.; Sun, Q.; Jena, P. Phys. Rev. Lett. 2017, 119, 046403. (27) Huang, B.; Jin, K. H.; Zhuang, H. L.; Zhang, L.; Liu, F. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 115117. (28) Gruznev, D. V.; Bondarenko, L. V.; Matetskiy, A. V.; Mihalyuk, A. N.; Tupchaya, A. Y.; Utas, O. A.; Eremeev, S. V.; Hsing, H. R.; Chou, J. P.; Wei, C. M.; Zotov, A. V.; Saranin, A. A.; et al. Sci. Rep. 2016, 6, 19446−9. (29) Gruznev, D. V.; Zotov, A. V.; Saranin, A. A. Jpn. J. Appl. Phys. 2017, 56, 08LA01−8. (30) Zhang, X.; Cui, B.; Zhao, M.; Liu, F. Phys. Rev. B: Condens. Matter Mater. Phys. 2018, 97, 085422. (31) Denisov, N. V.; Chukurov, E. N.; Luniakov, Y. V.; Utas, O. A.; Azatyan, S. G.; Yakovlev, A. A.; Zotov, A. V.; Saranin, A. A. Surf. Sci. 2014, 623, 17−24. (32) Gruznev, D. V.; Rao, B. V.; Tambo, T.; Tatsuyama, C. Appl. Surf. Sci. 2002, 190, 134−138. (33) Hashimoto, M.; Nakaguchi, A.; Guo, F. Z.; Ueda, M.; Yasue, T.; Matsushita, T.; Kinoshita, T.; Kobayashi, K.; Oura, M.; Takeuchi, T.; Saito, Y.; Shin, S. al. et. Surf. Sci. 2015, 641, 121−127. (34) Park, J. W.; Kang, M. H. Phys. Rev. Lett. 2012, 109, 166102. (35) Pickard, C. J.; Needs, R. J. J. Phys.: Condens. Matter 2011, 23, 053201. 4345

DOI: 10.1021/acs.nanolett.8b01341 Nano Lett. 2018, 18, 4338−4345