Letter pubs.acs.org/NanoLett
Topological Dangling Bonds with Large Spin Splitting and Enhanced Spin Polarization on the Surfaces of Bi2Se3 Hsin Lin,*,† Tanmoy Das,‡ Yoshinori Okada,§,∥,⊥ Mike C. Boyer,§ W. Doug Wise,§ Michelle Tomasik,§ Bo Zhen,§ Eric W. Hudson,§ Wenwen Zhou,∥ Vidya Madhavan,∥ Chung-Yuan Ren,#,∇ Hiroshi Ikuta,⊥ and Arun Bansil† †
Department of Physics, Northeastern University, Boston, Massachusetts 02115, United States Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States § Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ∥ Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, United States ⊥ Department of Crystalline Materials Science, Nagoya University, Nagoya 464-8603, Japan # Department of Physics, National Kaohsiung Normal University, Kaohsiung 80201, Taiwan ∇ TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom ‡
ABSTRACT: We investigate the topological surface state properties at various surface cleaves in the topological insulator Bi2Se3, via first principles calculations and scanning tunneling microscopy/spectroscopy (STM/STS). While the typical surface termination occurs between two quintuple layers, we report the existence of a surface termination within a single quintuple layer where dangling bonds form with giant spin splitting owing to strong spin−orbit coupling. Unlike Rashba split states in a 2D electron gas, these states are constrained by the band topology of the host insulator with topological properties similar to the typical topological surface state, and thereby offer an alternative candidate for spintronics usage. We name these new states “topological dangling-bond states”. The degree of the spin polarization of these states is greatly enhanced. Since dangling bonds are more chemically reactive, the observed topological dangling-bond states provide a new avenue for manipulating band dispersions and spin-textures by adsorbed atoms or molecules. KEYWORDS: Topological insulators, dangling bonds, Bi2Se3, scanning tunneling spectroscopy, electronic structures
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spintronics, and for the realization of many topological quantum phenomena.5,13−17 Some of the most exciting topological phenomena require electronic structure engineering such as proximity to magnetism or superconductivity.14−17 Unsaturated dangling bonds may modify topological surface bands and add tunability. Furthermore, how robust the metallicity of the topological surface states is, and the details of how Dirac states are affected by dangling bonds are important questions. Here we predict the emergence of “topological dangling bonds” on the surface of the threedimensional topological insulator material Bi2Se3 by firstprinciples calculations and confirm these predictions experimentally with scanning tunneling spectroscopy data. The “topological dangling bond” state by construction renders connection between valence and conducting bulk bands and thus remains immune to backscattering due to defects. We also expose a huge band splitting and its spin polarization in the
he development and performance of functional nanoscale materials and devices rely on thoroughly characterizing carrier transport properties at the material boundaries. Due to the inevitable loss of translational symmetry at the crystal edge, numerous chemical and quantum phenomena arise at surfaces. Two such edge states that have attracted great attention in fundamental research and applications are dangling bonds1−4 and topological surface states.5−13 The study of dangling bonds has been an ongoing subject of research for many decades mainly due to its tremendous importance in material growth (especially nanosized) processes,1 device fabrication, and semiconductor,3 and graphene4 device operations. Dangling bonds are chemically highly reactive and unstable, and these unsaturated states may trap electrons or holes, significantly impacting transport properties. On the other hand, topological band theory5−8 guarantees the existence of metallic surface bands for any surface termination of a topological insulator in the presence of time-reversal symmetry. The electric charges at the boundaries of topological insulators are programmed by band topology to resist backscattering when they encounter a time-reversal invariant defect.9 These topological surface states are of interest in quantum information, quantum processing, © 2013 American Chemical Society
Received: November 7, 2012 Revised: April 4, 2013 Published: April 24, 2013 1915
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to most likely be surfaces S4 and S5. In this work we focus mainly on region II (S4). The first-principles calculations were performed with the linear augmented-plane-wave (LAPW) method using the WIEN2K package25 and the projected augmented wave method26 using the VASP package27 within the framework of the density functional theory (DFT). The generalized gradient approximation (GGA)28 was used to describe the exchangecorrelation potentials. In addition to the bulk band computations, which were used to generate the projected bulk states, we have used a symmetric slab of six quintuple layers to simulate the surface electronic structure. Those states in the slab calculations whose energies fell inside the projected bulk band gap were identified as surface states. The results of WIEN2k and VASP were found to agree well with each other in this respect. The total-energy optimization of the lattice parameters and the atomic positions was performed using VASP, but the experimental crystal structures were used in the final computations presented in this study because they yield results in better accord with the measurements. We have previously established the viability of this approach in connection with the analysis of surface termination S1 by showing good agreement between the theoretical surface band dispersion and angle-resolved photoemission experiments.11 Unlike the termination S1 which only breaks weak van der Waals type of interlayer bonding, a termination within the quintuple layer breaks strong atomic bonds and may therefore host dangling bonds. As shown in Figure 1d, our first-principles calculations find that charges at S1 terminations are distributed over the first quintuple layer and part of the second quintuple layer, similar to previous work.29 On the other hand, charges in S4 surface states are more localized on the outmost Se and Bi layers (Figure 1e). While part of the charge lies between Bi and Se atoms, consistent with their covalent nature, the outmost triangle shape of the charge distribution is arranged with tips pointing toward the removed Se atom position (Figure 1f). This clearly reflects the dangling-bond character of the S4 surface state. To visualize the in-plane charge distribution we show the top view of the S4 plane in Figure 1h which reveals a triangular shape of the charge distribution of the dangling-bond states. On the contrary, there is no such dangling bond feature on S1. We can understand the emergence of these dangling bonds from a microscopic perspective. In the illustrative case of the S4 surface (Figure 1b), Se and Bi atoms from two adjacent layers each contribute one unpaired electron before cleaving. The resulting pair of electrons is shared by them to form a strong covalent bond. The cleaving process leaves an unpaired electron and therefore a highly reactive unsaturated bond on the surface atoms. Within the quintuple layers, Bi2Se3 can be viewed as a rock-salt structure with a rhombohedral distortion along the 111 direction. Each atom in the rock-salt structure is bonded to its six nearest neighbors by three pairs of p-orbitals, which are mutually orthogonal in rock-salt structure but become slightly distorted in Bi2Se3. Even in the presence of surface termination, these directional bonds are strong enough to more or less maintain the atomic positions between the top layer and the second layer of atoms, preventing the reconstruction of the surface as seen in our STM images of Figure 1a. We now discuss the surface states in these new terminations from the perspective of the topological band theory. The strong spin−orbit coupling in Bi2Se3 stipulates a band inversion at the
topological dangling bonds which are highly desirable for spindependent electronic functions.18−20 Bi2Se3 is a 3D topological insulator with a considerably large bulk gap of 330 meV.10−12 It belongs to the rhombohedral crystal structure with the space group D53d(R3m ̅ ), similar to the other topological insulators Bi2Te3 and Sb2Te3. The unit cell consists of five layers (quintuple layers) (Figure 1b). The
Figure 1. Surface terminations of Bi2Se3 and dangling bonds. (a) Constant current topography image showing four flat regions. (b) Schematic diagram illustrating the atomic layers of Bi2Se3. Each quintuple layer terminates at the single Se atomic layer (denoted as S1). Cleaving at S1 requires the breaking of weak Se−Se bonds, while the other surfaces require the breaking of strong Bi−Se bonds. (c) A diagonal cut between point A and B in a clarifies the sharp jumps between each flat regions. (d−h) Theoretical charge distributions have distinct features for S1 and S4 terminations. The charge density is calculated by integrating out the energy window of the bulk insulating gapwhich allows us to encode most of the surface states. The side views (d and e) are taken from the cuts along directions in the black dashed lines in top views (g and h). Blue and red balls indicate the positions of Bi and Se atoms, respectively.
stacking order of two consecutive quintuple layers can be represented as Se-Bi-Se-Bi-Se−Se-Bi-Se-Bi-Se. Figure 1b illustrates various possible surface terminations labeled S1− S5. The coupling is stronger between two atomic layers within one quintuple layer, but much weaker, predominantly of the van der Waals type, between two quintuple layers. Correspondingly, S1 has been the most common surface termination in this material both theoretically10,11 and experimentally.11,12,21−23 In our work, we use STM to study the surface of Bi2Se3. The experiments were carried out with home-built variable-temperature STM.24 The Bi2Se3 sample was cleaved in ultrahigh vacuum, and all f the measurements shown in this paper were acquired at 6 K with a Pt−Ir-tip. The STS spectra were taken with the same settings: Vsample = −400 mV, I = 200 pA. STM topography of the surface shown in Figure 1a reveals four distinct flat regions labeled I, II, III, and IV, respectively. A comparison of step heights with the structure of the quintuple layers allows us identify the termination of these planes. The vertical distance between regions I and IV matches the height of two quintuple layers. Region I and IV can be identified with surface termination S1. Regions II and III represent new surface terminations within the quintuple layers which are previously unexplored. Based on topographic measurements, they appear 1916
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Brillouin zone (BZ) center, making it a strong topological insulator according to the Fu and Kane classification scheme.8 Topological band theory guarantees the existence of metallic surface bands on any surface termination of Bi2Se3, as long as time-reversal symmetry is preserved. In other words, the conduction band and valence bands have to be connected by surface bands for all surface terminations, making the energy spectrum of the surface states span the bulk energy gap. Figure 2a and b provides examples of two such connections. On the
Figure 2. Schematic diagrams of the various possible surface bands. The bulk conduction and valence bands (blue area) are connected by the surface bands (red lines) between two time-reversal-invariant points Γ and M. The orange lines in c are trivial surface bands which fail to make such connections.
contrary, trivial surface bands (orange line) in Figure 2c fail to connect the bulk states and have nothing to do with the nontrivial topological phase. We note here that, when two surface state bands meet each other at the time-reversalinvariant points, either Γ or M, no gap is opened due to the protection accorded by time-reversal symmetry. The question now arises whether the dangling bond states can inherit the topological properties of the bulk material. To distinguish such states from trivial dangling bonds, we call these new states “topological dangling bonds”. Similar to usual topological surface states, topological dangling bond states would be expected to participate in connecting the bulk conduction bands and valence bands, making the spectrum of nontrivial topological surface states span the entire bulk energy gap. It is well-known both theoretically10,11 and experimentally11,12,21−23 that the S1 surface termination hosts singleDirac-cone surface bands. Here we study the development of surface states at S3 and S4. To best describe the dangling bond progression, we study their evolution with and without spin− orbit coupling via first-principles computations as shown in the second and first rows of Figure 3, respectively. The blue shaded region envelops all of the projected bulk energy bands, while the white background indicates bulk energy gaps. The Fermi level resides in the bulk gap for an insulator. However, the real Bi2Se3 samples are found to be electron-doped, and the position of Fermi level will be determined later via STS spectroscopy. Without spin−orbit coupling, a direct band gap is present at the Γ point10,11 (top row in Figure 3). At surface termination S1, which lies at the top of a quintuple layer, no surface state or dangling bond develops in Figure 3a, consistent with the weak coupling between two adjacent quintuple layers. For S3 and S4, surface states form inside the bulk gap with a dangling bond character. Without spin−orbit coupling, these dangling bonds do not connect the conduction and valence bands. They are spin degenerate and topologically trivial. Turning on spin−orbit coupling launches dramatic adjustments within the bulk states and thereby introduces characteristic surface band topology. The indicator of a nontrivial topological phase transition in the bulk bands is the development of an inverted band dispersion between the conduction and the valence states near the Γ point
Figure 3. Band structure evolution at different surface terminations with and without spin−orbit coupling and unconventional spintextures of topological dangling bonds states. The upper panels a, b, and c give theoretical band structures without spin−orbit coupling for the three cases of surface terminations S1, S4, and S3, respectively. The blue shadings represent the projected bulk bands, and the red lines are the surface states. The corresponding lower panels d, e, and f give the same results but with spin−orbit coupling. (g) A large 2D Fermi surface occurs at a chemical potential which intersects one surface state. Due to spin-helicity, backscattering is completely prohibited on this single-sheet Fermi surface. (h) The Fermi surface at a representative chemical potential at which multiple Fermi surface sheets appear. In this case, backscattering becomes enabled. The green and yellow arrows illustrate two backward scattering vectors which are, respectively, allowed and forbidden by spin-momentum locking.
when spin−orbit coupling is turned on. This is a robust signature tied to the Z2 nontrivial topology of the bulk bands, which guarantees metallic band dispersion on the surface (not a dangling bond). The existing dangling bonds at S3 and S4 now split via spin−orbit coupling. However, as explained above, the inversion and time-reversal symmetry of the host band topology constrains these two opposite spin states to meet at the Γ and M points. As a result, we obtain no gap at the Γ and M points, and the surface bands span the entire bulk energy gap, connecting both bulk conduction and valence band which is an indicator of the topological nature of the dangling bonds. In this way, the dangling bonds at S3 and S4 get promoted into the previously uncharted territory of intrinsic “topological dangling bonds”. While the surface states on S3 and S4 all possess the dangling bond character with large weight on the first and second surface atomic layers, the surface states near the Γ point are found to extend deeper into the solid compared to the surface states away from the Γ point. These results suggest that the Dirac-cone type surface states hybridize with typical dangling bond states around the Γ points, so that the topological dangling bond states possess both the dangling bond character and the Dirac-cone band dispersion. Next, we take a closer look at the large spin-split topological dangling bonds surface states on the termination S4 and discuss 1917
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exhibit such a linearly dispersing feature below the Fermi level and resemble previous STS results. As shown in Figure 4a, there is a good overall accord between the theoretical local density of states (LDOS) of regions I and IV and a typical experimental dI/dV spectrum. This agreement not only identifies the surface termination of region I and IV to be S1 but also pins down the position of the Fermi level, which lies about 40 meV above the conduction band minimum, and of the Dirac point which is estimated to lie at a binding energy of 390 meV. For terminations S3 and S4, multiple surface states result in a complicated theoretical LDOS in the bulk gap energy region as shown in Figure 4b. In particular, the blue curve for S4 termination in Figure 4b displays a prominent peak around the Fermi energy (zero bias). Despite the limited energy range of the STS data in Figure 4c, it is interesting that we also find a peak in dI/dV in region II, consistent with our earlier identification of this region as being S4 termination in connection with Figure 1 above. We emphasize that, in sharp contrast to the S4 surface, the calculated LDOS for S1 and S3 terminations in Figure 4b is quite smooth with little structure over the binding energy window of ±40 meV, suggesting that our STS spectra provide some experimental support for the existence of our theoretical predictions, differences between the detailed shapes of the theoretical LDOS and the experimental spectrum notwithstanding.32,33 Further experimental work using spin-resolved photoemission spectroscopy is however needed to clearly establish the existence of the novel topological surface states predicted in this study. Unlike the peak structure in the vicinity of an impurity site in other complex materials including d-wave high-temperature copper-oxide superconductors,34 graphene,35 and magnetically doped topological insulators,22,23 the peak structure in S4 is not local but extends over the entire region II as shown in Figure 4d. The spectra are homogeneous, and no surface reconstruction is observed. We note that, since the density of states at the Fermi level is higher in S4, the topological dangling bonds may supply a higher density of spin polarized current for spintronics applications and provide a playground for electron−electron correlations for future studies. We have demonstrated that the surface state bands on various surface terminations in the topological insulator Bi2Se3 are gapless, even when the surface termination hosts dangling bonds, providing further evidence of the topological robustness of the surface states. Importantly, we have found a new scenario where dangling-bond states participate in making the connection between the conduction and valence bands, thereby transforming them into topological surface states. The added advantage of topological dangling bond states is that they host giant spin-splitting and can render either a single large Fermi surface or multiple Fermi surfaces which can be useful for spindependent transport measurements. The degree of the spin polarization can achieve a very high value of 80%. Furthermore, dangling bonds are chemically reactive and therefore provide additional tunability, which can be achieved by incorporating atoms or molecules in or on the surface.
the possibility of a practical realization of the topologically guided transport of dangling bond carriers which are immune to backscattering. The binding energy dependence of the band splitting and spin-momentum interlocking in the dangling-bond surface states owing to spin−orbit coupling is illustrated in Figure 3e for the termination S4. The two bands with opposite spins are degenerate at the Γ and M points and spin split away from these time reversal invariant points. The spin splitting can be as large as 290 meV. Such a large value cannot be easily obtained in a free-electron-like Rashaba system. If the Fermi level is tuned into the center of the gap region, we achieve a single piece of Fermi surface of dangling bond character with left-handed spin helicity which carries the topologically nontrivial Berry phase of π. Although some departure from perfect in-plane spin-helicity is observed here due to the hexagonal warping effect30 or higher-order Dresselhaus spin− orbit coupling,31 backscattering (yellow horizontal line) is completely eliminated. Such a nondegenerate single piece of Fermi surface is the hallmark of a topological insulator and cannot be obtained in a Rashba system. It is interesting to point out that the volume of the Fermi surface on termination S4 is larger than that of typical topological surface states on termination S1. The density of states is at least 1 order of magnitude larger (Figure 4b). Thus, the backscattering-free
Figure 4. Local density states of various surface terminations. (a) A typical experimental dI/dV curve for region I and IV is shown as the solid red line. The theoretical local density of states are shown as a dashed magenta line. (b) The theoretical local density of states for various surface terminations are obtained from the first six quintuple layers. (c) The averaged experimental dI/dV is obtained for region II. The inset shows the conductance map around Fermi energy, where peak becomes prominent. (d) STM spectra for region II are shown along the cut between point A and B in the inset.
spin current could be enhanced for surface transport experiments on the termination S4. At higher energies, multiple pieces of Fermi surfaces can be obtained (Figure 3g). Here, the presence of more than two states along the same direction in the momentum-space restores backscattering processes. Our results imply the possibility of a gating controlled spin current. Moreover, the degree of the spin polarization of the topological dangling bond states can be as high as 80%, which is much higher than that of the typical topological surface states on the S1 surfaces. These functionalized properties put the topological dangling bond state at an advantage for practical applications more than other heavy-electronic semiconductors or 2D electron gas proposed for spintronics usages.18−20 To test our theoretical predictions, we obtained STS data that can provide spectroscopic fingerprints of the density of states at various cleaved surfaces. Previous STS measurements21,22 have demonstrated a linear differential conductance (dI/dV) in the gap region dominated by the linearly dispersing surface states. Our spectra I and IV (Figure 4a) generally
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Addresses
M.C.B.: Department of Physics, Clark University, Worcester, Massachusetts 01610, United States. 1918
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(22) Alpichshev, Z.; Biswas, R. R.; Balatsky, A. V.; Analytis, J. G.; Chu, J.-H.; Fisher, I. R.; Kapitulnik, A. Phys. Rev. Lett. 2012, 108, 206402. (23) Okada, Y.; Dhital, C.; Zhou, W.; Huemiller, E. D.; Lin, H.; Basak, S.; Bansil, A.; Huang, Y.-B.; Ding, H.; Wang, Z.; et al. Phys. Rev. Lett. 2011, 106, 206805. (24) Boyer, M. C.; Wise, W. D.; Chatterjee, K.; Yi, M.; Kondo, T.; Takeuchi, T.; Ikuta, H.; Hudson, E. W. Nat. Phys. 2007, 3, 802. (25) Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties; Karlheinz Schwarz, Techn. University Wien, Austria, 2001. (26) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953. Kresse, G.; Joubert, J. Phys. Rev. B 1999, 59, 1758. (27) Kress, G.; Hafner, J. Phys. Rev. B 1993, 48, 13115. Kress, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15; Phys. Rev. B 1996, 54, 11169. (28) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (29) Zhang, W.; Yu, R.; Zhang, H.-J.; Dai, X.; Fang, Z. New J. Phys. 2010, 12, 065013. (30) Fu, L. Phys. Rev. Lett. 2009, 103, 266801. (31) Basak, S.; Lin, H.; Wray, L. A.; Xu, S.-Y.; Fu, L.; Hasan, M. Z.; Bansil, A. Phys. Rev. B 2011, 84, 121401R. (32) Notably, the computed LDOS for the S4 termination in Figure 4b displays an asymmetry such that the LDOS is low at positive energies and high at negative energies around the Fermi energy. This asymmetry is opposite to that seen in the experimental spectrum in Figure 4c. In order to better assess this discrepancy, a full computation of the tunneling spectrum, which properly accounts for effects of the tunneling matrix element, will need to be carried out because STS intensities can be modified quite strongly by the tunneling matrix element.33 (33) Nieminen, J.; Lin, H.; Markiewicz, R. S.; Bansil, A. Phys. Rev. Lett. 2009, 102, 037001. (34) Hudson, E. W.; Pan, S. H.; Gupta, A. K.; Ng, K.-W.; Davis, J. C. Science 1999, 285, 88. (35) Ugeda, M. M.; Brihuega, I.; Guinea, F.; Gómez-Rodriguez, J. M. Phys. Rev. Lett. 2010, 104, 096804.
E.W.H.: Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, United States. Y.O.: WPI-Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank M. Z. Hasan for discussions. This research was supported in part by a Cottrell Scholarship awarded by the Research Corporation and by the MRSEC and CAREER programmes of the NSF. The work at Northeastern University is supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences contract DE-FG02-07ER46352, and benefited from Northeastern University’s Advanced Scientific Computation Center (ASCC), theory support at the Advanced Light Source, Berkeley and the allocation of supercomputer time at NERSC through grant number DEAC02-05CH11231. C.Y.R. gratefully acknowledges NSC, NCTS, and NCHC of Taiwan for financial and technical support.
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