Multiple Coexisting Dirac Surface States in Three-Dimensional

Multiple Coexisting Dirac Surface States in Three-Dimensional Topological Insulator PbBi6Te10

Marco Papagno,*,† Sergey V. Eremeev,‡,§,∥ Jun Fujii,⊥ Ziya S. Aliev,¶,∇ Mahammad B. Babanly,¶ Sanjoy Kr. Mahatha,■ Ivana Vobornik,⊥ Nazim T. Mamedov,∇ Daniela Pacilé,† and Evgueni V. Chulkov○,◆,§,∥ †

Dipartimento di Fisica, Università della Calabria, 87036 Arcavacata di Rende, Calabria, Italy Institute of Strength Physics and Materials Science, 634021 Tomsk, Russia § Tomsk State University, 634050 Tomsk, Russia ∥ Saint Petersburg State University, Saint Petersburg 198504, Russia ⊥ CNR-IOM, TASC Laboratory, AREA Science Park Basovizza, 34149 Trieste, Italy ¶ Institute Catalysis and Inorganic Chemistry, Azerbaijan National Academy of Science, AZ1143 Baku, Azerbaijan ∇ Institute of Physics, Azerbaijan National Academy of Science, AZ1143 Baku, Azerbaijan ■ Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, 34149 Trieste, Italy ○ Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Basque Country, Spain ◆ Departamento de Física de Materiales UPV/EHU, Centro de Física de Materiales CFM−MPC and Centro Mixto CSIC-UPV/EHU, 20080 San Sebastián/Donostia, Basque Country, Spain ‡

ABSTRACT: By means of angle-resolved photoemission spectroscopy (ARPES) measurements, we unveil the electronic band structure of three-dimensional PbBi6Te10 topological insulator. ARPES investigations evidence multiple coexisting Dirac surface states at the zone-center of the reciprocal space, displaying distinct electronic band dispersion, different constant energy contours, and Dirac point energies. We also provide evidence of Rashba-like split states close to the Fermi level, and deeper M- and Vshaped bands coexisting with the topological surface states. The experimental findings are in agreement with scanning tunneling microscopy measurements revealing different surface terminations according to the crystal structure of PbBi6Te10. Our experimental results are supported by density functional theory calculations predicting multiple topological surface states according to different surface cleavage planes. KEYWORDS: topological insulator, Dirac surface states, ARPES, STM, DFT

T

The layered compounds of Bi2Se3-type has drawn special attention because these 2 -TIs have a single Dirac cone at Γ̅ , which resides in a relatively large inverted bulk energy gap and free of dangling bond states owing to weak van der Waals coupling between structural layers. Most of the known TIs of the Bi2Se3-type are binary or ternary quintuple-layer (QL) or septuple-layer (SL) structured compounds that were theoretically predicted and experimentally confirmed.12−23

he nontrivial bulk band topology originated from the inversion of the normal band ordering owing to large spin−orbit interaction (SOI) in three-dimensional topological insulators (TIs) is characterized by nonzero (nontrivial) 2 topological invariants.1−5 The nontrivial 2 guarantees the existence of an odd number of gapless spinhelical topological surface states (TSSs) in the bulk energy gap. The topological surface states are protected by time reversal symmetry and thus remain gapless in a nonmagnetic environment. As a result of these unique properties, TSSs are of interest for the observation of many novel quantum phenomena.6−11 © 2016 American Chemical Society

Received: December 9, 2015 Accepted: February 19, 2016 Published: February 19, 2016 3518

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and V-shaped bands coexisting with TSSs. The experimental findings are supported by the predictions from the DFT calculations, which also evidence different spatial charge density distributions of the topological surface states.

Other TI materials belonging to the same family are ternary compounds that are formed by alternating QL and SL units.20 In this case, nonequivalent QL- and SL-surface terminations are possible. These surface terminations support Γ̅ Dirac states that, in consequence of the complicated bulk band inversion, differ in Dirac point energy, band dispersion, and spatial charge density localization. An example of such a material is PbBi4Te7 compound,20,24 in which, owing to the presence of both QLand SL-surface terminations, two Dirac cones can be resolved in the angle-resolved photoemission spectroscopy (ARPES) spectrum. In contrast to PbBi4Te7 composed of simple alternating QL and SL units, the crystal structure of PbBi6Te10 comprises SL and two QL building blocks in the hexagonal unit cell (Figure 1a). For such a crystal structure three cleavage planes are

RESULTS AND DISCUSSION Figure 1b is a representative topographic image (400 × 200 nm2) of as cleaved PbBi6Te10 surface displaying the low-energy electron diffraction pattern (LEED) in Figure 1d. In Figure 1c, the apparent height profile along the line in Figure 1b is shown. Two kinds of steps with apparent height of about 1.20 nm and 1.70 nm are found, corresponding to the predicted height of the QL and SL unit of the PbBi6Te10 crystal,20 and in agreement with STM measurements on the parental PbBi4Te7 compound.24 The STM measurements prove that the two steps alternate themselves in a QL-QL-SL-QL-QL-SL-... sequence, confirming the presence of three different surface terminations: 5L, 5−5L, and 7L. A statistical analysis covering a total area of more than 100 μm2 of the sample surface reveals approximately the same amount of the three surface terminations. Figure 2a−b present the experimental ARPES intensity map collected with 25 eV photon energy along the K̅ −Γ̅ −K̅ and M̅ −Γ̅ − M̅ directions for PbBi6Te10; we also report the corresponding energy distribution curves in Figure 2c−d. These data clearly evidence three main linearly upward dispersing features, with a minimum at the Γ̅ point. In accordance with our DFT calculations (see below) and with previous works,20 we assign these features as follow: the most inner linearly dispersing feature as 7L-derived topological surface state, the middle one and the outer one to the 5L- and 5−5L-induced TSSs, respectively. The overlap of both the 5L and 5−5L TSSs with the bulk bands in the energy region 0.35 ÷ 0.50 eV below EF does not allow an accurate experimental determination of the Dirac point energies. However, by linear interpolation of the 5L feature (not shown) we estimate the Dirac point energy DP5L ≃ − 0.48 eV. On the other hand, the Dirac point is well-resolved for the 7L terminated surface and allows estimation of the Dirac point energy: DP7L = −0.36 eV. The TSSs of the three surface terminations display almost linear dispersion up to the Fermi level along the Γ̅ −K̅ direction, whereas distortions along the Γ̅ −M̅ direction (red arrows in Figure 2b) of the 5L- and 7L-derived cones are observed at about k∥ = 0.10 Å−1 and ≃−0.26 eV for the 5L-state and at k∥ = 0.08 Å−1 and ≃ − 0.20 eV for the 7L-state. This change of the 5L and 7L Dirac cone slope is due to the rhombohedral crystal structure25 of PbBi6Te10 and is seen clearly in the calculated spectrum where the Dirac cone comes into the bulk projected region (Figure 3). The 7L, the 5L, and the 5−5L features cross, along the Γ̅ −K̅ direction, the Fermi level at momentum k∥ = 0.13 Å−1, 0.18 Å−1, and 0.23 Å−1, respectively. The TSSs display similar group velocity of the Dirac Fermions close to EF. By momentum distribution curve fitting, we estimate the group velocity along Γ̅ −K̅ direction for each feature, resulting in v7L ∼ 4.5 × 105 m/s, v5L ∼ 5.3 × 105 m/s, and v5−5L ∼ 4.8 × 105 m/s; These values are in good agreement with the group velocity estimated on other topological surface states.21,26,27 In Figure 2a−b, we also observe diffuse photoemission spectral-weight intensity at about 20 meV below the Fermi at the Γ̅ point, which we assign to the bottom of the conduction band. On the other hand, our measurements do not allow a

Figure 1. (Color online) (a) Atomic structure of PbBi6Te10 compound; Red dashed-line rectangle marks the hexagonal cell, blue dashed lines show different cleavage planes (cl.1, cl.2a, and cl.2b). (b) Constant-current STM image on fresh cleaved PbBi6Te10 (VB = 1.0 V; It = 0.2 nA; T = 300 K; size 400 nm × 200 nm). (c) Apparent height profile along the black line in (b) revealing the presence of terraces with different step height due to different surface terminations. (d) Low-energy electron diffraction pattern on PbBi6Te10 collected with an electron beam of 55 eV.

possible: cl.1 (in between two equivalent QL units) and two others, cl.2a and cl.2b (in between nonequivalent SL and QL blocks). The cl.1 cleavage gives rise to QL-terminated surface with SL block beneath, the cl.2a cleavage results in formation of QL-terminated surface on top of double QL blocks and finally, cl.2b resulting in SL-terminated surface. Following to designation of ref 20, we will refer to the three surface terminations as 5L, 5−5L, and 7L. The appearance of different types of terraces in tetradymite-like layered crystals is expected to result in the formation of distinct and coexisting topological surface states. In the present work, we examine, for the first time, the electronic band structure of PbBi6Te10 by ARPES measurements accompanied by scanning tunneling microscopy (STM) measurements, and accurate density functional theory (DFT) calculations. STM measurements confirm distinct cleavage planes at the surface in agreement with the atomic structure of PbBi6Te10 compounds. High-resolution ARPES measurements provide evidence of the coexistence of multiple Dirac topological surface states at the zone-center, displaying distinct electronic band dispersion, constant energy contours, and Dirac point energies. We also experimentally demonstrate the presence of a two-dimensional Rashba-type split states, M3519

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clear determination of the valence band maximum due to the faint spectral-weight intensity of the valence band at the zonecenter. Nevertheless, we expects such maximum to be located at about 300 meV below EF. The nature of the TSSs are further revealed by the constant energy contours displayed in panels e−g of Figure 2. At EF (lower side of Figure 2e), the 5−5L band displays a faint nearly hexagonal photoemission intensity contour reflecting the nearly 6-fold symmetry of the system. The area enclosed by the nearly hexagonal contour decreases for higher energies (Figure 2f−g), and then progressively turns into a circular-shape contour for E−EF ⩾ 0.28 eV. The 5L- and 7L-derived states display similar constant energy contours, in particular the characteristic snowf lake pattern is observed for energies from EF down to about −0.20 eV for both features. This particular shape highlights a strong warping of the 5L- and 7L-Dirac state, in analogy with parental compounds.20,24 The snowf lakes progressively turn into a circular contour centered at the Γ̅ point with smaller radius and progressively reduced spectral-weight intensity for E−EF ⩾ 0.28 eV. The main features of the measured TSSs are captured by the calculated spin-resolved surface electronic band structure for charge neutral PbBi6Te10, presented in Figure 3a. Here, we combined spectra for three surface terminations. In agreement with earlier prediction,20 each surface termination (7L, 5L, and 5−5L) supports the Dirac topological surface state. In particular, the 7L surface shows a rather linear dispersion close to its DP7L, which lies about 60 meV above the Γ̅ valence band edge, in agreement with the experimental value of ∼80 meV. The Dirac point of the 5L TSS lies at about 40 meV lower than DP7L, closer to the bulk valence states, consistently with the estimated experimental value of 120 meV. At the same time the 5L TSS deviates markedly from the linear dispersion approaching the Dirac point. The Dirac point of 5−5L termination (DP5−5L) emerges below (∼15 meV) the first valence band so that the Dirac cone loses its localized character passing through the narrow energy region of the first valence band and becomes localized (and spin-polarized) again in the local gap between the first and second bulk valence bands. However, this state persists linear dispersion everywhere above the DP, except typical Γ̅ −M̅ warping in the vicinity of the

Figure 2. (Color online) ARPES raw band structure for PbBi6Te10 along the (a) K̅ −Γ̅ −K̅ and (b) M̅ −Γ̅ −M̅ directions. Dotted lines in panel (a) track the dispersion of Rashba-like states and arrows in (b) identify distortions in the electronic band dispersion of the 5Land 7L-derived TSSs. (c) and (d) Corresponding energy distribution curves of (a) and (b), respectively. Unsymmetryzed constant energy ARPES maps measured at (e; lower side) the Fermi level, (f) E−EF = 0.20 eV, and (g) E−EF = 0.28 eV. Black, violet, and green lines in the upper side of panel (e) mark the DFT simulated energy contour at 0.36 eV above the predicted DP7L for 7L, 5L, and 5−5L terminations, respectively.

Figure 3. (Color online) (a) Calculated band structure of PbBi6Te10 surfaces along the K̅ −Γ̅ −M̅ direction with 7L, 5L, and 5−5L terminations (black, violet, and green lines, respectively); size of color circles represent weights of the states in the surface layers; red and blue colors denote the sign of in-plane spin components (positive and negative, respectively), whereas shaded area identifies the bulk-projected bands. Band spectrum of PbBi6Te10 for individual (b) 7L, (c) 5−5L, and (d) 5L surface terminations. The size of orange and violet circles represents the weight of the state in the surface and subsurface building blocks, respectively. Shaded area outlines the bulk-projected bands. 3520

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Figure 4. (Color online) ARPES raw experimental band structure for PbBi6Te10 along the K̅ −Γ̅ −M̅ direction collected with (a) 21 eV, (b) 25 eV, and (c) 50 eV photons energy. (d−f) Second derivative with respect to the energy of the ARPES data presented in panels (a-c), in the energy region from −0.3 eV down to −1.20 eV below EF.

To further investigate the electronic states of PbBi6Te10, we have performed ARPES measurements by using different photon energy. In Figure 4a−c, we present ARPES maps collected along K̅ −Γ̅ −M̅ with 21, 25, and 50 eV photons energy, respectively. These measurements prove that the dispersions of the three TSSs are barely affected by the change of the photon energy, thus strongly supporting the largely 2D nature of these states. We observe, however, that the spectralweight of the TSSs varies with photon energy and, for a fixed photon energy, is asymmetric along the two high-symmetry directions. These effects may be related to matrix element effects in the photoemission process28 but may also be induced by the spatial localization of the topological surface states. In particular, along the Γ̅ −M̅ direction, the 5−5L and 5L states are expected to be mainly localized in subsurface SL block, that is, at a depth of ≈10 ÷ 25 Å below the surface, whereas with the photon energy used here, only the electronic states of the topmost layers are probed. Figures 2 and 4 also evidence additional states in the energy region ∼0.2 ÷ 0 eV below the Fermi level at the zone-center. These states display a parabolic-like dispersion (gray markers in Figure 2a) with a minimum energy of 0.17 eV below EF at the momentum offset of ± k0, with k0 = 0.035 Å−1. These results suggest a Rashba-like character of the parabolic bands, similarly to the spin-splitting observed in surface states of semiconductors29,30 and of noble metals.31 In these cases, the characteristic parameters quantifying the strength of the Rashba splitting are the momentum offset k0, the Rashba energy ER, and the coupling constant αR (Rashba parameter). These parameters are related, in the case of an ideal two-dimensional electron gas, by the following equations ER = ℏ2k20/2m* and k0 = m*αR/ℏ2. For the measurements presented here, we estimate

conduction band. The Dirac TSSs resided on different terminations demonstrate the same (clockwise) spin helicity above the DP and the opposite one below it. The general good agreement between theory and experiment is proved in Figure 2e. Here, we show along with the experimental constant energy contours (lower side of Figure 2e), the predicted one for each of the surface termination (upper side of Figure 2e), calculated at 0.36 eV above the predicted DP7L to get into account the experimental chemical potential. Calculations also evidence a set of narrow M-shaped bands at about 0.20 ÷ 0.35 eV and V-shaped valence states at 0.35 ÷ 0.55 eV below EF. The three topological surface states also identify themselves by different spatial localization. In particular, as one can see in Figure 3b−d, at 7L and 5−5L surfaces the TSS is almost completely localized within outermost building block, SL, and QL, respectively. An exception is the upper part of the 5−5L TSS branch in the Γ̅ −M̅ direction, which has a sizable weight in the subsurface QL. In contrast, the Dirac cone at the 5L surface (Figure 3d), being localized in subsurface SL block in the vicinity of the Γ̅ point, gradually changes its spatial localization from subsurface SL to outer QL with increasing energy. At energy about 70 meV above DP in Γ̅ −K̅ direction the TSS almost completely relocate into surface QL. In the Γ̅ −M̅ direction the weight of the TSS in the subsurface block decreases moving upward from DP but it does not completely relocate into the outermost QL. Thus, one can conclude that the deviation of the Dirac cone dispersion from the linear behavior within the band gap, as in the case of 5−5L TSS in upper Γ̅ −M̅ section and in the vicinity of DP for 5L TSS, can be associated with changes in spatial localization from surface to subsurface building block. 3521

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ACS Nano k0 = 0.035 Å−1 and ER = 0.03 eV, and we evaluate the Rashba parameter αR = 1.70 eVÅ. Similar Rashba-like states have also been observed in ARPES in others’ topologic insulators following aging effects or adsorption of foreign atoms.32−36 In both cases, the adsorbed species can produce a remarkable downward band bending inducing a two-dimensional potential electron gas with strong Rasba-type splitting. An alternative explanation is the expansion of van der Waals spacing in between the blocks that build-up the crystal caused by the intercalation of gases.37−39 Recently, it has been proposed that band bending can also induce quantization effects in the electronic states at deeper binding energy,33,34 resulting in a set of M-shaped replicated bands in the valence band spectra.33−36,39,40 Indeed, such M-shaped states are also observed in PbBi6Te10 compounds and can be highlighted by performing the second derivative of the ARPES plot as shown in Figure 4d−f. These data evidence M-shaped features in the energy range −0.40 ÷ −0.60 eV as well as multiple V-shaped bands in between −0.70 ÷ −1.20 eV below EF. Though extrinsic Rashba-like states, induced by foreign gases, are rather common among topological insulators, as are oxidebased compounds41 and heavy elements composed semiconductors,29 we argue that the observed set of M- and Vshaped bands may be intrinsic to PbBi6Te10 compounds. Confinement of electrons can indeed results in discrete quantized electronic states;42 however, our calculations in Figure 3 predict M- and V-shaped bands for each building block of the PbBi6Te10 crystal20 and narrow bulk M- and valence Vshaped states when all three surface terminations are present.

The presented measurements were performed on surfaces obtained by cleavage at room-temperature in ultrahigh-vacuum (UHV) conditions. The cleaved surfaces were stable for several days as long as the samples were preserved in UHV, namely, the overall ARPES key features and the Fermi energy level remain unchanged. The highquality single-crystalline (111) surface was verified by the sharp features in the LEED pattern and STM measurements. The presented ARPES and STM experiments were carried out at the APE-IOM beamline of the Elettra synchrotron radiation facility. This beamline allows to perform complementary ARPES and STM measurements on the same sample surface in UHV conditions. In order to unveil the electronic band structure of PbBi6Te10 we have performed detailed photon energy dependence ARPES investigations in the photon energy region 15 ÷ 60 eV at 77 K. STM measurements were carried out with a home-built roomtemperature scanning tunneling microscope. The electronic structure calculations were performed within the density functional theory implemented in VASP code.43,44 We used the all-electron projector augmented wave (PAW)45,46 basis sets with the generalized gradient approximation47 to the exchange correlation (XC) potential. Relativistic effects, including SOI, were taken into account. Unlike earlier calculations for this compound, the van der Waals corrections were included here. To take into account the effect of dispersion interactions, we use DFT-D3 method by Grimme48 as implemented in the VASP code. Both lattice parameters and internal atomic positions were optimized in this approach. We have used a 7 × 7 × 7 and 9 × 9 × 1 k-point grids for bulk and slab self-consistent calculation, respectively. To simulate the surfaces, we used over 40 atomic layers symmetric slabs to avoid the interactions between opposite surfaces. The slab thicknesses were 44, 51, and 58 atomic layers for 5−5L, 5L, and 7L terminations, respectively. The vacuum space between slabs was about 15 Å.

AUTHOR INFORMATION CONCLUSIONS In conclusion, the surface electronic structure of the PbBi6Te10 compound has been unveiled by ARPES measurements. STM investigations reveal three-distinct surface terminations that result in multiple coexisting Dirac cones centered at the Γ̅ point of the reciprocal space and with largely 2D character in the ARPES spectra. These states display different electronic dispersion and distinct constant energy contours. We also experimentally observe Rashba-like split surface states close to the Fermi level, and characteristic M- and V-shaped bands at deeper energy. Supported by ab initio calculations, our experimental observations help in the understanding on the diversity of topological surface states in TIs and may pave a way for the application of the topological insulator to the real spintronic devices.

Corresponding Author

*E-mail: marco.papagno@fis.unical.it. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We acknowledge partial support from the Basque Country Government, Departamento de Educación, Universidades e Investigación (Grant No. IT-756-13), the Spanish Ministerio de Ciencia e Innovación (Grant No. FIS2010-19609-C02-01), the Ministry of Education and Science of Russian Federation (Grant No. 2.8575.2013), and Saint Petersburg State University (project 15.61.202.2015). Numerical calculations were performed on the SKIF-Cyberia supercomputer at the National Research Tomsk State University.

METHODS Single crystalline ingot of PbBi6Te10 was grown from nonstoichiometric composition by the vertical Bridgman−Stockbarger method. The synthesis was performed in two steps. First, the polycrystalline composition was synthesized from high-purity (5N) elements in evacuated quartz ampule at about 1000 K for 8 h mixing incessantly, followed by air cooling. Afterward, the polycrystalline sample was placed in a conical-bottom quartz ampule, which was sealed under a vacuum better than 10−4 Pa. At the beginning of the growing process, the ampule was held in the “hot” zone (≈ 920 K) of a two-zone tube furnace for 24 h for a complete melting of the composition. The charged ampule moves from the “hot” zone to the “cold” zone with the required rate 1.0 mm/h. In this way, bulk ingot with average dimensions of ≈4 cm in length and 0.8 cm in diameter was obtained. The single crystal structure of the as-grown PbBi6Te10 ingot was verified by accurately X-ray diffraction and scanning electron microscope measurements.

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DOI: 10.1021/acsnano.5b07750 ACS Nano 2016, 10, 3518−3524