arXiv:1306.3310v1 [cond-mat.mtrl-sci] 14 Jun 2013 lcrncsrcue[] u tcnb rae nboth on created be can complicated it more but this Bi [8], show structure not electronic do temperature room hnemnfssisl sasito l h ad to bands the all of shift a spectra as ARPES itself that manifests early change observed Bi been has from struc- It electronic the for ture. crucial are relaxations structural 7]. 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(different interlayer terminations surface bilayer-terminated the the for of notation indication with crystal 2 Se-Se ulem led iv Ribeiro, Silva Almeida Guilherme Se2 Se1 Bi2 Bi1 sGri,31390Bl oiot,M,Brazil MG, Horizonte, Belo 30123-970 Gerais, as ybt ehiusaei odagreement good in are techniques both by ao Bi lator prtr.Bt prahsso that show approaches Both mperature. fial,a lentv emnto ya by termination alternative an ifically, 1 eSa oa e-e,M,Brazil MG, S˜ao Jo˜ao Del-Rei, de oahnRawle, Jonathan 00Aru ,Denmark C, Aarhus 8000 , termination quintuple layer 2 to ftevndrWasgap Waals der van the of ation Se 2 Se 3 3 sdtrie ylow-energy by determined is E ntdKingdom United DE, oices h a e al gap Waals der van the increase to stry, 5 n hlpHofmann Philip and d d d d d 3 Se1-Se1 Bi-Se1 Se2-Bi Bi-Se1 Se1-Bi oizHoesch, Moritz 1 da Avellar Edmar termination Bibilayer 3 Chris 2 2 Se isare ties 3 (111) k 2

A detailed structural determination of the Bi2Se3(111) 2 surface cleaved at room temperature is therefore called TABLE I: LEED Pendry R-factor and SXRD χ for different trial models and for non-optimised (truncated bulk) as well for and presented here. We use two complementary as optimised parameters. and powerful structural techniques, low-energy elec- 2 tron diffraction (LEED) and surface X-ray diffraction LEED RP SXRD χ (SXRD). Model Bulk Optimised Bulk Optimised The Bi2Se3 crystals were grown by standard methods Se1 0.74 0.25 3.15 2.44 described elsewhere [9]. The bulk structure was deter- Bi1 0.83 0.61 9.50 4.68 mined by X-ray diffraction at room temperature. To Se2 0.91 0.70 30.32 10.20 this end, a fine powder was filed from the crystal rod Bi2 0.80 0.65 30.31 7.02 and diffraction experiments were performed on a STOE Se-Se 0.98 0.80 9.46 7.05 powder diffractometer using Cu K 1 radiation in trans- α Bi atop [5] 1.00 0.84 11.88 6.31 mission geometry. The bulk structure parameters were analysed by Rietveld refinement and found to be in good agreement with the literature [17]. These structural pa- rameters were used as starting and reference points for SXRD crystal truncation rod intensities were extracted the surface structure determination. LEED and SXRD by numerically integrating the background-subtracted experiments were performed in ultra-high vacuum (UHV) spot in a well defined region of interest on the detector chambers with a base pressure of ≈ 10−10 Torr. The image. The structure factors were calculated by apply- samples were cleaved at room temperature in a loadlock ing correction factors to account for the polarisation of with a somewhat inferior pressure. X-ray photoemission the X-ray beam, the rod interception, and the area of spectroscopy performed in the LEED chamber did not the sample contributing to the scattered intensity, and show any detectable contaminations. SXRD data were then taking the square root of the corrected intensity taken at beamline I07 of the Diamond Light Source, us- [27]. Subsequent analysis of the data was undertaken ing 20 keV X-rays and a UHV chamber mounted on a using the ANAROD code [28]. large ’2+3’ diffractometer [18]. Scattered X-rays were The structure determination was performed by a quan- collected using a two-dimensional detector (Pilatus) en- titative comparison between the experimental and theo- abling fast data acquisition. The specular reflectivity (00 retical I(V) curves and crystal truncation rod intensities. rod) was collected using a conventional Θ − 2Θ scan, The agreement between experimental data and model whilst all non-specular data was recorded using a fixed calculations was quantified using the Pendry reliability ◦ 2 X-ray incidence angle of 1 . Note that data were ac- factor (RP ) [29] and by χ for LEED and SXRD, re- quired over a time span in the order of hours, whereas spectively. In the first step of the structure analysis, five Ref. [5] reports an increased Bi concentration near the bulk truncated trial models were tried: the different pos- surface, interpreted as a bilayer formation, immediately sible possible bulk terminations (Se1, Bi1, Se2, Bi2, and after cleaving the sample at room temperature. Se-Se, see Fig. 1) as well a bismuth bilayer atop of the Full dynamic LEED I(V) model calculations were per- truncated bulk crystal. The resulting agreement is shown formed using a modified version of the Symmetrised Au- Table I. After that, an optimisation procedure was used tomated Tensor LEED (SATLEED) computer package to adjust the structural parameters as well as the in- [19, 20]. The potential and the electron scattering phase- ner potential (for LEED) to find the optimum structure, 2 shifts for the Bi2Se3 (111) surface were calculated using namely the one that leads to the lowest Rp or χ . For the the optimised muffin-tin potential method [21], an ap- LEED analysis of the Se1 structure, the surface Debye proach recently used to successfully determine complex temperatures of the first four layers were refined, too, but metal oxide surfaces [22–24]. Specific phase-shift sets this gave only rise to a very small change of RP . The fi- 2 were calculated for selenium and for bismuth atoms, de- nal values of Rp and χ for all structural models are also pending on their surface and bulk positions. The I(V) listed in Table I. Regarding the Bi bilayer atop model model calculations converged when using 12 phase shifts [5], all the nine stacking possibilities were tested and the (lmax = 11); and 13 phase shifts were used in the final structural parameters of the bilayer were refined. The 2 calculations. Convergence for a lower number of phase best values of RP and χ are given in Table I. The final shifts than in e.g. Ref. [25] is probably caused by two comparison between measured and calculated diffraction factors: one is the different method of phase shift calcula- data are shown in Figures 2 and 3, both for the best fit tions and the other is the lower maximum electron energy obtained with the intact QL (Se1 ) termination as well in the experiment, which was found sufficient due to the as for the best agreement that can be reached with an higher temperature. Debye temperatures were obtained optimised Bi bilayer termination. from Ref. [26]. The real and imaginary parts of the opti- For both LEED and SXRD, the termination with an cal potential were set to V0 = 10.0 eV and V0i =-5.0 eV, intact QL, i.e. the Se1 model, gives the best agree- respectively. ment between experimental and simulated diffraction 3

Experiment TABLE II: Interlayer distances found from LEED and SXRD (2.0) intact QL (Se1) (see Fig. 1) and the corresponding bulk distances. All values Bi bilayer are in given in Angstroms.˚ The uncertainties for the bulk values are smaller than 0.01 A.˚ (0,2) Interlayer Distances Bulk Value LEED SXRD dSe1−Bi 1.62 1.56 ± 0.03 1.51 ± 0.05 (1,1) dBi−Se2 1.95 1.96 ± 0.03 1.94 ± 0.06 dSe2−Bi 1.95 2.01 ± 0.04 1.91 ± 0.05 dBi−Se1 1.62 1.53 ± 0.05 1.72 ± 0.04 dSe1−Se1 2.42 2.51 ± 0.08 2.50 ± 0.06 (1,0)

intensityunits) (arb.

finding a small contraction in the first interlayer spacing (0,1) dSe1−Bi and a small expansion of the van der Waals gap distance dSe1−Se1. From the results of this structural determination, we 100 200 300 can draw the following conclusions: Both techniques electron kinetic energy (eV) unambiguously show that, at room temperature, the Bi2Se3(111) surface is terminated with an intact QL FIG. 2: LEED experimental and theoretical I(V) curves for rather than covered by a Bi bilayer. An intact QL termi- the best structural model. The inset shows the LEED pattern nation also suggest that this termination prevails at lower at 161 eV. temperature, since less thermal activation energy is avail- able for a major structural rearrangement. The observed Experiment termination is at variance with the recent low-energy ion intact QL (Se1) Bi Bilayer scattering result report in Ref. [5] but consistent with other experimental evidence. Notably, the surface elec- tronic structure for a Bi bilayer on Bi2Se3(111) is quite different [7] from the simple single Dirac cone observed for the surface terminated by a van der Waals gap. While only low-temperature ARPES data for an on-purpose Specular prepared bilayer of Bi on Bi2Se3(111) are available, it CTR(00l) CTR(23l) is unlikely that a room temperature measurement such as in Ref. [8] would miss the electronic structure change

and the additional bands caused by the bilayer. Finally,

Structure factor (a.u.) factor Structure it is interesting to note that a recent room temperature SXRD structural determination of thin Bi2Te3 films on Si has a also shown the films to have a intact QL termi- nation towards vacuum [30]. The details of the surface relaxations are also inter- CTR(11l) CTR(12l) esting. The contraction of the first interlayer spacing dSe1−Bi is of the order of 5% and such a large contraction l (reciprocal lattice units) is unusual for a closed packed surfaces. On closed-packed simple metal surfaces, small expansions of the first inter- FIG. 3: SXRD data from four different crystal truncation layer spacing are more frequently found than contractions rods (CTRs) and fit to two different terminations. [31]. On Bi2Te3(111), a small contraction of 1 % was re- ported [25]. More importantly, neither LEED nor SXRD find a significant expansion on the first van der Waals data. The detailed structural relaxations for this ter- gap spacing. Both point towards a small expansion in mination are given in Table II. The agreement between the order of 4 %, far smaller than the expansions of 20 the two structural techniques is excellent, apart from the - 40 % required to explain the observed two-dimensional third interlayer distance dSe2−Bi where LEED finds a electronic states in the conduction band as caused by slightly larger expansion than SXRD, and the fourth in- an interlayer expansion [11, 12]. This can be taken as terlayer distance dBi−Se1 where LEED points towards a additional evidence that band bending, an not surface small contraction of the interlayer spacing whereas SXRD relaxation, is the cause for the appearance of new two- shows an expansion. Both techniques are consistent in dimensional electronic states near the surface of Bi2Se3 4

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