Evolution of Topological Surface States in Antimony Ultra-Thin Films

Yao, Guanggeng; Luo, Ziyu; Pan, Feng; Xu, Wentao; Feng, Yuan **; Wang, Xue-sen

doi:10.1038/srep02010

Evolution of Topological Surface States in Antimony Ultra-Thin Films

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Published: 18 June 2013

Volume 3, article number 2010, (2013)
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Scientific Reports

Evolution of Topological Surface States in Antimony Ultra-Thin Films

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Guanggeng Yao¹,
Ziyu Luo¹,
Feng Pan¹,
Wentao Xu¹,
Yuan ** Feng¹ &
…
Xue-sen Wang¹

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Abstract

Based on an inverted bulk band order, antimony thin films presumably could become topological insulators if quantum confinement effect opens up a gap in the bulk bands. Coupling between topological surface states (TSS) from opposite surfaces, however, tends to degrade or even destroy their novel characters. Here the evolution and coupling of TSS on Sb(111) thin films from 30 bilayers down to 4 bilayers was investigated using in-situ Fourier-transform scanning tunneling spectroscopy and density functional theory computations. On a 30-bilayer sample, quasi-particle interference patterns are generated by the scattering of TSS from the top surface only. As the thickness decreases, inter-surface coupling degrades spin polarisation of TSS and opens up new wavevector-dependent scattering channels, resulting in spin degenerate states in most part of the surface Brillouin zone, whereas the TSS near the zone centre exhibit little inter-surface coupling, so they remain spin-polarised without opening a gap at the Dirac point.

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Introduction

Recent experimental^1,2,3,4,5 and theoretical^6,7,8 works have demonstrated that topological surface states (TSS) support massless spin-polarised Dirac fermions due to a strong spin-orbit coupling effect. They are robust and immune to backscattering by non-magnetic defects because of protection by time-reversal symmetry⁹. Unlike the Dirac fermions in graphene with pseudospin texture, the real helical spin polarization TSS exhibit has been widely studied by surface-sensitive experiments such as angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) as summarized in recent review articles^10,11. TSS are attractive not only in fundamental condensed matter physics for realising novel entities such as dyons¹², imaging magnetic monopoles¹³ and Majorana fermions^12,14, but also in practical applications in spintronics and error-tolerant quantum computing. Motivated by such perspective, special attention has been focused on thin films hosting TSS suitable for device applications. Therefore, three-dimensional (3D) topological insulator (TI) thin films approaching 2D limit have been explored. Theoretical calculations predict that an energy gap can be opened at the Dirac point by inter-surface coupling¹⁵. Some of these films may exhibit quantum spin Hall effect as that observed in HgTe quantum wells^16,17. Experimental studies on Bi₂Se₃^18,19 and Bi₂Te₃²⁰ confirm the existence of a thickness-dependent bandgap. However, the detail of inter-surface coupling effect, especially the intermediate state between weak and strong coupling of surface states (SS) from two surfaces, still needs to be interrogated. From topological nontrivial to trivial phases, interesting transformation must take place progressively as the overlap of electron wave functions on two surfaces increases with reducing film thickness.

Here we investigate the inter-surface coupling issue in antimony (Sb), which has a rhombohedral crystal structure and can be considered as a stacking of (111) bilayers (BL, 1 BL = 3.75 Å). There are several reasons to study Sb(111) films. Firstly, as the “parent” of the first-generation 3D TI Bi_1−xSb_x²¹, although bulk Sb is semimetal due to its negative indirect bandgap, its band order is inverted at the L point of the Brillouin zone. Sb(111) has been confirmed to possess TSS, leading to the absence of 180° backscattering and exotic transmission through atomic steps²². Next, the strongly distorted TSS Dirac cone on Sb(111) yields various scattering channels in QPI patterns, from which TSS dispersion and spin information can be extracted. Measuring the patterns at different film thickness helps us understand how the spin texture evolves as inter-surface coupling varies. Thirdly, a thin film with a large surface-to-volume ratio can make surface effect more observable. Lastly, compared with well-studied compound TIs such as Bi₂Se₃, Sb thin films provide a single-element simple system for demonstrating topological properties without much influence of residual bulk carriers from self-do** states^2,4,23 or spatial fluctuations of charge and potential²⁴. Therefore, by using Fourier-transform scanning tunneling spectroscopy (FT-STS), we measure the quasi-particle interference (QPI) patterns of TSS on thick and thin Sb(111) films. Combining with density functional theory (DFT) calculations, we aim to identify the scattering features in the patterns generated by the intra- and inter-surface couplings of TSS and to examine the dependence of the couplings on film thickness and wavevector k.

Results

We grew Sb films on Si(111)-√3 × √3:Bi-β surface in an ultrahigh vacuum (UHV) chamber^25,26,27,28. Shown in Figure 1a is a STM image of an Sb(111) film of thickness ~30 BL. Steps here are all 3.75 Å corresponding to 1 BL of Sb(111). The atomic resolution image in the inset exhibits the hexagonal lattice on the (111) surface. In Fig. 1b, a typical differential tunneling conductance dI/dV_b spectrum, where V_b is sample bias voltage and I the tunneling current, is displayed to reveal the local density of states (LDOS) of electrons in certain energy range. Unlike Bi₂Se₃ and Bi₂Te₃, Sb(111) has a strongly distorted TSS Dirac cone, with its lower part bowing up rapidly near point of the first surface Brillouin zone (SBZ) before bending down to merge with bulk valence bands, as shown schematically in Fig. 1b inset. Several extraordinary features of Sb(111) show up starting from the Dirac point E_D at E ≈ −240 meV (with the Fermi energy E_F at E = 0), which have also been confirmed by previous ARPES measurements^1,29. The specific dispersion of TSS on Sb(111) allows us to determine E_D being at the appearance E of QPI patterns^{22,Fig. 2c–d.}

Full size image

When Sb(111) film is thin enough, however, the TSS on the top and bottom surfaces will couple eventually. It is normally believed that a gap will open up at the Dirac point and the Dirac cone will turn into Dirac hyperbola when the coupling is significant^15,18. In order to gain insight into how the thickness affects the band structure and furthermore, the coupling of SS from two surfaces, we examined a 9-BL Sb(111) film. Interestingly, according to DFT calculations, at this thickness, the coupling of states at is not strong enough to open a gap yet, but the inter-surface coupling of states elsewhere in k-space is already significant as revealed by FT-STS map**. Shown in Fig. 4a is the QPI pattern on 9-BL Sb(111) at E = 20 meV. Compared with the 30-BL sample, a few changes are obvious in the pattern. Firstly, besides intensity mostly along in the 30 BL case, here comparable intensity along can also be seen. Secondly, instead of discrete q for 30-BL Sb, 12 lobes of continuous intensity with clear cutoff vectors labeled as q_Eand q_F along and , respectively, are observable on 9-BL Sb, indicating new scattering channels are effective.

Discussion

Now we discuss the origins of these new scattering channels on 9-BL Sb. Notice the scale difference between Fig. 2c and Fig. 4a. The new intensity lobes in Fig. 4a have q lengths longer than those in Fig. 2c. Specifically, the lengths of the cutoff vectors q_Eand q_F (both shown as dash-line arrows) are 0.63 Å⁻¹ and 0.54 Å⁻¹, respectively, whereas q_C = 0.25 Å⁻¹ in Fig. 2c. The q_E/q_Flength ratio takes a unique value 1.17 in the measured energy range. For comparison, the calculated CEC at E_F is shown in Fig. 4b, with superficial spin directions labeled as grey arrows assuming the upper surface separated far from the lower one. The new scattering channels are also marked in Fig. 4b, with q_E between the outer edges of opposite hole pockets along and q_F between the outer edges of next-nearest-neighbor hole pockets. Such assignments yield a , in agreement with the measured ratio. These scatterings, especially q_E, however, seem to violate spin conservation based on the superficial spin texture.

Different from thick film case, the two surfaces of 9-BL film are separated not far from each other, so a SS is no long confined to one surface. Now, it is possible for an electron in state k on one surface to scatter into a state with the same spin on the opposite surface. In another viewpoint, for a thick Sb(111) film, there is one TSS Dirac cone on each surface. With time-reversal and inversion symmetries, a pair of SS of a particular k are degenerate in energy but with opposite spin. They do not couple noticeably with each other since their wave functions overlap little. In a thin Sb(111) film, the coupling becomes strong if wave function overlap is significant, yielding mixing states with their spin only partially polarized or even totally degenerate. This opens up new scattering channels without violating spin conservation. Therefore, quite different from the 30-BL film where the patterns mainly originate from the so-called “intra-surface scattering”, here the QPI patterns include “inter-surface scattering”. On the other hand, the intensities in inner hexagonal zone in Fig. 4a corresponding to q_Aand q_B scatterings marked in Fig. 4b are stronger than those of q_E and q_F. This part overlaps closely with the QPI patterns on the 30-BL sample, demonstrating significant contribution from intra-surface scattering. This two-part pattern clearly shows the coexistence of intra- and inter-surface scattering events.

Based on DFT computation results of CEC and spin texture near E_F, we simulated the QPI pattern as shown in Fig. 4c, which is in good agreement with our experimental pattern in Fig. 4a. First of all, the characteristic outer lobes of comparable intensities along and are reproduced in the simulation pattern. Secondly, the core part of the simulated pattern has stronger intensity along , which is consistent with out observation that “intra-surface scattering” is still nontrivial. It is also worth noting that the experimental patterns were taken at 4.2 K with a 5 mV peak-to-peak modulation added to V_b, which results in an energy resolution ΔE ≈ 4.5 meV³². If this energy window is considered, the dots and arcs in the simulation pattern should be smeared out to continuous features similar to those in Fig. 4a.

Besides new features in QPI patterns, following the procedure described by Bian et al.^33,34, the spin separation of SS can be defined and evaluated for our 9 BL Sb(111) film. In Fig. 4d, the electronic states in the 9 BL film obtained with DFT computation are plotted along . The SS bands remain cross each other at , i.e., the Dirac point is intact. Due to quantum confinement effect, an indirect bandgap of ~0.3 eV can be observed for the bulk bands in Fig. 4d. Simple estimation based on bulk band parameters³⁵ gives a bandgap ~0.53 eV, whereas Zhang et al. get a value of 0.25 eV in their computations^6,8, so they can be considered as true surface states. Sb(111) has a highly warped Dirac cone. The SS not far from penetrate quite deep into the interior and they almost behave as surface resonance states. In 9-BL Sb(111), the inter-surface coupling of these states makes them locate more near the film centre than at the surfaces. The spin splitting of SS due to the Rashba effect, which depends on the overall potential gradient ∇V the electrons experience, is greatly reduced. To the extreme, for those states with k ≥ 0.5 Å⁻¹ in Fig. 4f with wave functions totally symmetric about the film centre, the overall ∇V = 0, so the spin polarisation is completely lost. Therefore, our results demonstrate that SS spin polarization diminishes not only with decreasing film thickness, but even more dramatically with k moving from to .

Although not an ideal TI, Sb(111) ultrathin films allow us to investigate the extraordinary scatterings between SS with nearly parallel spin directions, while in other TIs (e.g. Bi₂Se₃) possessing an ideal Dirac cone it is hard to get similar features exclusively between SS. The “distorted” Dirac cone and dramatic k-dependent penetration depth of SS in Sb thin films offer us an interesting quasi-2D system to help interpret the detailed evolution of coupling and hybridization of TSS. The dramatic change in QPI patterns with film thickness indicates that the intra- and inter-surface coupling of TSS dominates in the thick and thin film cases, respectively. The inter-surface coupling of TSS in a “thin” film shows strong k-dependence. The tuneability of relative contributions of intra- and inter-surface scatterings by changing thickness can be further explored for tailoring the surface energetic and transport properties for potential applications.

Methods

The experiments are carried out in a UHV LT-STM system. The base pressure is better than 1 × 10⁻¹⁰ Torr. Clean Si(111)-7 × 7 surface is prepared by degassing at 500°C overnight, a briefing annealing at 850°C and finally flashing at 1200°C for ~1 min. The Si(111)-√3 × √3:Bi-β surface serving as the substrate for Sb film growth in this work is prepared with 2-ML Bi deposition on Si(111)-7 × 7 at room temperature followed by annealing at ~450°C for 15 min. Bi and Sb deposition fluxes are generated from Ta boats loaded with high purity (99.999%) source materials. Prior to the deposition, the evaporators are degassed at appropriate temperature for a few hours in order to remove contaminations. Bi deposition flux is calibrated by measuring the coverage and thickness of Bi(110) films on Si(111). 1 ML of Bi(110) represents 9.3 × 10¹⁴ atom/cm². Sb is deposited on Si(111)-√3 × √3:Bi-β at 100°C to form (111)-oriented thin films with thickness from 4 BL to >30 BL. All STM images are acquired at 77 K or 4.2 K. The dI/dV_b spectra are acquired at 4.2 K using a lock-in amplifier with a modulation voltage at a frequency of 700 Hz and a peak-to-peak amplitude of 5 mV. The dI/dV_b map** for FT-STS is normally taken in a square area of edge length ~25–40 nm, without any atomic step and other defect in the area.

First-principles DFT-based electronic structure calculations are performed using the VASP package³⁸ with a plane wave basis and a 5 × 5 k-point sampling of the Brillouin zone. In all calculations, generalized gradient approximation (GGA) in Perdew-Burke-Ernzerhof (PBE) format³⁹ and spin-orbital coupling are included. The neighbouring Sb(111) film slabs are separated with a 10-Å vacuum region along the [111] direction.

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Acknowledgements

We acknowledge the financial support from Singapore MOE AcRF grant (T208B1110), A*STAR SERC (Project No. 122-PSF-0017) and NUS RGF grants R-398-000-008-112 and R-144-000-310-112.

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Department of Physics, National University of Singapore, 2 Science Drive 3, 117542, Singapore
Guanggeng Yao, Ziyu Luo, Feng Pan, Wentao Xu, Yuan ** Feng & Xue-sen Wang

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Guanggeng Yao
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Ziyu Luo
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Feng Pan
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Wentao Xu
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Yuan ** Feng
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Xue-sen Wang
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Contributions

G.Y., Y.P.F. and W.X. carried out the experiments; G.Y., Z.L., Y.P.F., W.X. and X.-S.W. analyzed the data; Z.L. and Y.P.F. carried out the theoretical calculations. Y.P.F. and X.-S.W. assisted in the theoretical analysis. G.Y. and X.-S.W. prepared the manuscript.

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Yao, G., Luo, Z., Pan, F. et al. Evolution of Topological Surface States in Antimony Ultra-Thin Films. Sci Rep 3, 2010 (2013). https://doi.org/10.1038/srep02010

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Received: 07 March 2013
Accepted: 31 May 2013
Published: 18 June 2013
DOI: https://doi.org/10.1038/srep02010
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Evolution of Topological Surface States in Antimony Ultra-Thin Films

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Topological phase transition and quantum spin Hall edge states of antimony few layers

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Introduction

Results

Discussion

Methods

References

Acknowledgements

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Topological phase transition and quantum spin Hall edge states of antimony few layers

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Evolution of Topological Surface States in Antimony Ultra-Thin Films

Abstract

Similar content being viewed by others

Topological phase transition and quantum spin Hall edge states of antimony few layers

Topological proximity effect in a topological insulator hybrid

Surface morphology and Raman spectroscopy of thin layers of antimony and bismuth chalcogenides

Introduction

Results

Discussion

Methods

References

Acknowledgements

Author information

Authors and Affiliations

Contributions

Ethics declarations

Competing interests

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About this article

Cite this article

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Topological phase transition and quantum spin Hall edge states of antimony few layers

Realization of Dirac Cones in Few Bilayer Sb(111) Films by Surface Modification

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