Robustness of a Topologically Protected Surface State in a Sb2Te2Se Single Crystal

A topological insulator (TI) is a quantum material in a new class with attractive properties for physical and technological applications. Here we derive the electronic structure of highly crystalline Sb2Te2Se single crystals studied with angle-resolved photoemission spectra. The result of band mapping reveals that the Sb2Te2Se compound behaves as a p-type semiconductor and has an isolated Dirac cone of a topological surface state, which is highly favored for spintronic and thermoelectric devices because of the dissipation-less surface state and the decreased scattering from bulk bands. More importantly, the topological surface state and doping level in Sb2Te2Se are difficult to alter for a cleaved surface exposed to air; the robustness of the topological surface state defined in our data indicates that this Sb2Te2Se compound has a great potential for future atmospheric applications.

A topological insulator (TI) is a quantum material in a new class with attractive properties for physical and technological applications because of its potential in spintronic devices [1][2][3][4][5][6] . Two-dimensional (2D) TI are typically associated with gapless edge states; three-dimensional TI are associated with gapless surface states. The edge and surface states in these systems generally reveal a Dirac-cone-like dispersion; the spin degeneracy of Dirac fermions in these states of TI is removed and locked to the momentum, as these surface states of 3D TI exhibit a helical spin structure with the spin vectors parallel to the surface and perpendicular to momentum k. This unique topological phase offers a platform to realize diverse quantum phenomena, such as a topological magnetoelectric effect 7 , a Majorana fermion 8 , the quantum spin-Hall effect 9 and spintronic applications 10 .
A key to develop applications in topological quantum computing 7,11 and low-power spintronic devices 10 is that the dissipation-less surface states must be in the topological transport regime; specifically, the presence of an isolated Dirac cone is highly favoured because of the decreased scattering from bulk bands. Manipulating the position of the Dirac point in TI for future applications becomes a crucial problem. TI in the bismuth family -Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 -have a tetradymite structure, which consists of covalently bonded quintuple layers (QL) with a weak interaction through a van der Waals force within QL 12 . Bi 2 Se 3 and Bi 2 Te 3 have the chemistry of a non-stoichiometric compound 13,14 ; both compounds are invariably doped through the crystal defects, which results in the transport properties being affected by bulk carriers. A single crystal of Bi 2 Se 3 invariably exhibits a n-type doping behaviour because of the Se vacancies or anti-site defects 15,16 . Regarding the Bi 2 Te 3 compound, both n-type and p-type behaviour can be achieved on varying the initial composition to become either Bi-rich or Te-rich depending on growth conditions, which results in Te and Bi anti-site defects, but a Dirac point in Bi 2 Te 3 immersed in the bulk valence band can cause strong scattering from bulk carriers. In contrast, the Sb 2 Te 3 compound invariably behaves as a p-type semiconductor [17][18][19] . The position of the Dirac point is inherently located above the Fermi level, but the bulk valence band observed across the Fermi level in direction Γ − M is unfavour-able for an application of spintronic devices [18][19][20] , even though recent work demonstrated that the position of the chemical potential can be varied with the thickness of Sb 2 Te 3 thin films 21 . Additionally, Sb 2 Te 3 is an important p-type element in thermoelectric modules. In early work, Hicks and Dresselhaus proposed that low-dimensional systems could enhance the thermoelectric efficiency through an enlarged thermopower 22 , but a decreased thermopower value was observed in Sb 2 Te 3 thin films; the discrepancy was resolved in recent work on Sb 2 Te 3 thin films [23][24][25] . The separate contributions to thermopower from the bulk and the surface could cause a decreased total thermopower 26 . A surface state existing in the energy gap with a small concentration of bulk carriers could benefit an enhanced thermopower.
Authors of several theoretical and experimental works have focused on the predictions and findings of an isolated Dirac cone to decrease scattering from bulk carriers in ternary tetradymite-like topological insulators, such as Sb x Bi 2-x Se 2 Te and Bi 2-x Sb x Te 3-y Se y systems [27][28][29][30][31][32][33] , but experimental work on p-type Sb 2 Te 3-x Se x ternary topological insulators is lacking. A calculation indicated that a topological surface state still existed for x ≈ 0.94 27 . In previous work, only p-type doped behaviour in Sb 2 Te 2 Se was proposed 34 . A recent observation of the Zeeman effect in the topological surface state of Sb 2 Te 2 Se was reported 35 ; the g-factor of the topological surface state extracted from the Zeeman shift is disparate in Bi 2 Se 3 and Sb 2 Te 2 Se, but no experimental result for the band structure of Sb 2 Te 2 Se has been reported.
In the present work, we measured angle-resolved photoemission spectra (ARPES) of highly crystalline Sb 2 Te 2 Se and Sb 2 Te 3 single crystals. According to the measured band structure of Sb 2 Te 2 Se, an examination of angle-resolved photoemission spectra in an experiment dependent on photon energy indicated that the 2D behaviour of the topological surface state was unaffected. A maximum of the bulk valence band (BVB) near the Fermi level appeared in the middle of direction Γ − M, but no clear crossing at the Fermi level was observed. In direction Γ − K, no contribution about the Fermi level from the BVB was found; only a few contributions about the Γ point from the BVB in the Sb 2 Te 2 Se compound appeared. More importantly, we found that the doping level of Sb 2 Te 2 Se, unlike compounds Bi 2 Se 3 and Bi 2 Te 3 34,36 , is difficult to vary, even for a cleaved surface exposed to air. The robustness of a topological surface state in Sb 2 Te 2 Se benefits the control of electrical properties of fabricated devices. These results indicate that Sb 2 Te 2 Se can be an effective candidate to improve the performance of future spintronic and thermoelectric devices.

Results
Electronic structure of Sb 2 Te 2 Se. In a Sb-based ternary tetradymite-like topological insulator, Sb 2 Te 2 Se naturally crystallizes in a chalcogen-ordered structure with a Te-Sb-Se-Sb-Te QL, and has the stoichiometric composition of these materials. In the stacking order, the inversion symmetry is unbroken; the topological surface state persists. Highly crystalline single crystals of Sb 2 Te 2 Se and Sb 2 Te 3 were grown in a home-made resistively heated floating-zone (RHFZ) furnace. X-ray diffraction (XRD) and Raman scattering were applied to characterize the crystal quality (see Supplementary materials). The electronic structure of a Sb 2 Te 2 Se single crystal was derived using high-resolution ARPES. Figure 1a  indicates that the band-mapping result shows a highly crystalline quality of the present samples. The entire measured band structure agrees qualitatively with previously calculated results 28,37 and behaves in a typical p-type manner. In comparison with the band structure of Sb 2 Te 3 20 , the contribution of BVB of Sb 2 Te 2 Se around the Fermi level in the middle of branch Γ − M in our result and calculation show a strongly suppressed behaviour. The calculated result shows also a slight contribution of BVB from the bulk band projection around the Fermi level at the Γ point; an ARPES experiment dependent on photon energy was conducted to examine the contribution of BVB around the Γ point. We noticed that the energy scale between the Fermi level and the TSS in our result differs slightly from that in a preceding calculation. shows also a consistency with the recent result of the Landau-level (LL) spectra in Sb 2 Te 2 Se 35 . Additionally, the scattering from bulk carriers is strongly suppressed. Figure 1c shows plots of the photoemission intensity in momentum space with various constant energies at the Fermi level − 30, 60, 90, 120 and 150 meV; the spectra are recorded at photon energy 24 eV. Only a circular-like surface state is observed on the Fermi surface. At 30 and 60 meV, the bulk component appears in direction Γ − M and shows a three-fold symmetry. With increasing binding energy, a slight deformation of the TSS is observed in the images of constant energy mapping.
In the photoemission experiment, the normal component of electron wave vector k ⊥ of the initial state is based on a free-electron model in the final state 38 , in which E kin is the kinetic energy of the photoelectron and V 0 is the inner potential. To examine the property of a 3D bulk valence band, we conducted an ARPES experiment dependent on photon energy in a range from 12 to 42 eV, to cross several periods of the Brillouin zone (BZ) in the k z direction if the inner potential is assumed to be V 0 = 9.64 eV 39 . A k-space map in the bulk BZ plotted with varied photon energy at collecting angle ± 18° of the detector was used to explore the k z dependence of TSS, RSS and bulk bands (see Supplementary materials). The electronic structure of Sb 2 Te 3 was studied for comparison with the same Sb 2 Te 2 Se crystal. Figure 2a shows the band-mapping results of ARPES spectra in Sb 2 Te 3 (0001) along  Figure 3b shows plots of the band-mapping results in Sb 2 Te 3 along Γ − M; these results are similar to those reported 18,19,40 . The BVB1 in Sb 2 Te 3 has a clear band crossing at the Fermi level in the middle of Γ − M, which indicates that scattering from bulk carriers is greater than that in the Sb 2 Te 2 Se compound. Regarding the interaction of BVB and TSS about the Γ point, Fig. 4a,b display the photoemission intensity image of ARPES and the second derivative of the image in Sb 2 Te 2 Se respectively; these spectra were recorded at photon energy 22 eV. The BVB1 band appears to have a crossing with the TSS band. This result implies an orbital hybridization that can occur about the Γ point to be similar to that in previous work on Sb 2 Te 3 40 . A comparison of the photoemission intensity image in Sb 2 Te 3 along direction Γ − M is shown in Fig. 4c,d. The Rashba splitting of TSS in Sb 2 Te 3 is clearly observed in the plot of the second derivative of the photoemission intensity image, but in our spectra no splitting in Sb 2 Te 2 Se can be resolved. Additionally, in contrast to Sb 2 Te 3 , because a major contribution of charge carriers in Sb 2 Te 2 Se comes only from the BVB about the Γ point and because no other contribution is observed in BZ, the resistivity in Sb 2 Te 2 Se is expected to be larger than that in Sb 2 Te 3 .
The dependence of resistivity on temperature and Hall measurement at room temperature were measured, showing the resistivity in Sb 2 Te 2 Se to be ten times that in Sb 2 Te 3 (see Supplementary materials). The charge carrier number extracted from a Hall measurement near 296 K is 2.2 × 10 20 cm −3 for Sb 2 Te 3 and 3.1 × 10 19 cm −3 for Sb 2 Te 2 Se. A charge carrier number ~ 3.1 × 10 19 cm −3 in Sb 2 Te 2 Se indicates that it behaves as a heavily doped semiconductor, but the bulk carrier number in Sb 2 Te 2 Se still decreases significantly. These results show the consistency of our ARPES result. Because the position of the Dirac point can be manipulated on controlling the chemical composition of a topological insulator in the bismuth family TIs, a possibility to decrease the charge carrier number is to increase the content of Se atoms.
The efficiency of a thermoelectric cooler is generally described according to the value of the figure of merit, Z T , expressed as 42 , in which S is thermopower, σ is electrical conductivity and κ is thermal conductivity. To consider a two-band model of a TI, the total thermopower and electrical conductivity come from the surface state and the bulk carriers. The total electrical conductivity is expressible as σ total = σ bulk + σ surface ; the total thermopower is expressed as S total = (σ bulk S bulk + σ surface S surface )/σ total 26 . In a thin-film system, the contribution of electrical conductivity from bulk bands can be decreased on controlling the thickness of the TI. As Sb 2 Te 3 behaves as a p-type semiconductor, the maximum of the valence band is above the position of the Dirac point. The sign of the thermopower from the surface state and bulk are opposite if the position of the chemical potential is located above the Dirac point, which can result in a decreased thermopower. In contrast, more bulk carriers can increase the part of the thermal conductivity from the charge carriers if the position of the chemical potential is located below the Dirac point. Although the thermopower is increased, a greater thermal conductivity from bulk charged carriers confers no benefit to enhance the figure of merit. In our present Sb 2 Te 2 Se system, the maximum of the valence band is suppressed inherently below the Fermi level, which implies the same sign of the thermopower for charge carriers from the surface state and from the bulk valence band. Sb 2 Te 2 Se has a high potential as a p-type thermoelectric element, especially in an application of a hybrid thin-film heterostructure.
Robustness of a topological surface state. Surface reactivity is a crucial problem for a TI in the bismuth family, such as Bi 2 Se 3 and Bi 2 Te 3 . Previous work on the degradation of the surfaces of Bi 2 Se 3 and Bi 2 Te 3 shows that the doping level can be altered with gas or vapor contamination 34,36,[43][44][45] ; an extrinsic doping dependent on ambient environmental conditions in Sb 2 Te 3 was also studied with Hall measurements 46 ; this effect limits the potential applications in TI in the bismuth family. In the present work, experiments involving the deposition of oxygen and an air environment were performed to detect the robustness of the topological surface state in Sb 2 Te 2 Se. Figure 5a displays the resolution of core-level photoemission for a surface cleaved in situ and exposed to varied content of oxygen. No oxidation signal was observed after the deposition of oxygen about 1000 Langmuir (L) near 296 K. The band dispersions and the Fermi level-crossing vector of TSS and RSS before and after exposure were the same, which implies no impurity doping on the surface. Figure 5b displays the results of photoemission-mapping images after cleaving in situ in UHV and ex situ in an air environment. According to a comparison of these results, the image for the sample cleaved ex situ is only slightly smeared because of the surface pollution, but no change of the band position occurs, as shown in Fig. 5c. This result reveals the robustness of TSS in a Sb 2 Te 2 Se compound and indicates that this Sb 2 Te 2 Se compound has a high potential for applications in spintronic devices. In particular, the authors of a recent investigation proposed the possibility of tuning the doping level on varying the thickness of Sb 2 Te 3 21 . Further work on Sb 2 Te 2 Se becomes important.

Conclusion
For Sb 2 Te 2 Se single crystals of high quality that we grew, we studied the electronic structure of the Sb 2 Te 2 Se compound with ARPES. The results of band mapping reveal that this Sb 2 Te 2 Se compound is a p-type semiconductor and has an isolated Dirac cone. That the maximum of the bulk valence band in the middle of Γ − M is suppressed below the Fermi level implies a possibility of decreased scattering from that bulk valence band and that the thermopower can have the same sign for the surface state and the bulk carriers; the Sb 2 Te 2 Se system is hence a potential candidate for the future application of spintronic and thermoelectric devices. More importantly, the robustness of TSS in the Sb 2 Te 2 Se system benefits the control of the performance of the devices.

Methods
Crystal growth. Single crystals of Sb 2 Te 2 Se and Sb 2 Te 3 were grown in a home-made resistively heated floating-zone furnace (RHFZ). The initial raw materials Sb 2 Te 2 Se and Sb 2 Te 3 were mixed according to the stoichiometric ratios. The stoichiometric mixtures of highly pure elements Sb (99.995%), Se (99.995%) and Te (99.995%) were first melted at 850~950 °C and cooled to about 23 °C afterward in an evacuated silica tube. The material was used as a feeding rod for the following RHFZ experiment. The growth rate was 1.5 mm/h. After growth, the crystals were cooled to 23 °C over 50 h. Crystals of diameter 3.0 mm and length 30 mm were obtained reproducibly. A crystal cleaved along the basal plane showed a silvery, shiny, mirror-like surface.
ARPES. ARPES were measured at National Synchrotron Radiation Research Center in Hsinchu, Taiwan at beamline BL21B1 U9-CGM for spectroscopy. The photoemission spectra were measured in a UHV chamber equipped with a hemispherical analyzer (Scienta R4000, collecting angle ± 15°). The polarization vector was invariably in the angular dispersive plane. The single crystals were cleaved in situ and measured at a base pressure 5.1 × 10 −11 Torr. All spectra were recorded for samples at 83 K and with varied photon energy. The angular resolution was 0.2°; the energy resolution was better than 25 meV over the entire range of photon energy.
Regarding a test of the robustness of the topological surface state, single crystals of Sb 2 Te 2 Se were cleaved ex situ in air, followed by transfer to the load-lock chamber after 5 min. After pumping for 1 h, the cleaved crystal was transferred to the analysis chamber for the ARPES experiment.