Atomic structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ (111) surfaces probed by photoelectron diffraction and holography

Understanding how topologically protected surface states behave at surfaces and interfaces requires knowledge of the atomic structure. Whether the (111) surfaces of the prototypical topological insulators ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ are Bi or chalcogen terminated is the subject of current controversies. We employ photoelectron diffraction and holography, combining the advantages and avoiding the disadvantages of the contesting techniques previously used. We find bulklike chalcogen termination with a very small surface relaxation $\left(<1\%\right)$ in agreement with density functional theory simulations. We prove the chalcogen termination for cleaved crystals and epitaxial films which shows the robustness of our conclusions.

Figure 1

Experimental and EDAC simulated (for structure 1 with bulk parameters) XPD patterns obtained for the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface at different electron kinetic energies for the Se $3d$ (a) and Bi $4f$ (b) core levels. (c) Cross-sectional view of the ${\mathrm{Bi}}_2{\mathrm{X}}_3 \left(X=\text{Se,Te}\right)$ structure.

Figure 2

An example of the holographic reconstruction of a 3D-atomic structure for Se $3d$ obtained at a kinetic energy of 846 eV: an experimental XPD pattern (a); a real space image (b) and its cross section (c), a simulated XPD pattern (d), and a simulated real space image (e) obtained for the Se-terminated surface (structure 1).

Figure 3

Contributions of different atomic positions of an Se emitter to the diffraction pattern and the real space image presented in Fig. 2: left column, emitter position (marked as atoms in ring); middle column, calculated XPD pattern for a given emitter; right column, calculated real space image for a given emitter.

Figure 4

Different surface structures, the corresponding Bi $5d$ spectra, and Bi $4f$ and Se $3d$ diffraction patterns. $R$-factor values describing the correlation with experimental data are provided. The calculated chemical shifts are given for certain atomic layers relative to bulk.

Figure 5

An example of the $R$-factor chart for the interatomic distances $d_1$ and $d_2$ optimization for the Se $3d$ diffraction pattern at an electron energy of 846 eV in the case of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$.

Figure 6

High resolution ARPES dispersions of the TSS, bulk conduction band (BCB) and bulk valence band (BVB) states of (a) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and (b) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ obtained at photon energy of 21 eV and a temperature of 30 K.

Figure 7

Experimental (a,c) and EDAC simulated (structure 1 with bulk parameters [17]) (b,d) XPD patterns obtained for the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface at different electron kinetic energies for the Te $4d$ (a,b) and Bi $4f$ (c,d) core levels.

Figure 8

$R$-factor chart for the interatomic distances $d_1$ and $d_2$ optimization for the Bi $4f$ pattern obtained at 742 eV for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$.