Geometric and electronic structure of the Cs-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface

Using surface x-ray diffraction and scanning tunneling microscopy in combination with first-principles calculations, we have studied the geometric and electronic structure of Cs-deposited ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface kept at room temperature. Two samples were investigated: a single ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystal, whose surface was Ar sputtered and then annealed at $\sim 500{}^{\circ }\mathrm{C}$ for several minutes prior to Cs deposition, and a 13-nm-thick epitaxial ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film that was not subject to sputtering and was annealed only at $\sim 350{}^{\circ }\mathrm{C}$. In the first case, a considerable fraction of Cs atoms occupy top layer Se atoms sites both on the terraces and along the upper step edges where they form one-dimensional-like structures parallel to the step. In the second case, Cs atoms occupy the $fcc$ hollow site positions. First-principles calculations reveal that Cs atoms prefer to occupy Se positions on the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface only if vacancies are present, which might be created during the crystal growth or during the surface preparation process. Otherwise, Cs atoms prefer to be located in $fcc$ hollow sites in agreement with the experimental finding for the MBE-grown sample.

Figure 1

(a)–(e): Experimental (symbols) and calculated (lines) structure factor amplitudes along several crystal truncation rods for about 0.4 ML of Cs atoms deposited on a single crystal ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface at room temperature. The best fit represented by solid lines follows the data in all details; some disagreement is only observed at very deep minima, where the experimental resolution is not sufficient. The (red) dashed lines represent the structure factor amplitudes calculated for the model in which 0.4 ML of Cs are located in the vdW gap site. (f): Plot of $|F_{\mathrm{obs}}|$ versus $|F_{\mathrm{calc}}|$ for all 1104 reflections (best fit — red symbols, vdW model — dark pink symbols). The diagonal line represents the ideal condition $|F_{\mathrm{calc}}|=|F_{\mathrm{obs}}|$.

Figure 2

Schematic of the SXRD derived Cs adsorption site geometry on single crystalline (a) and on MBE grown ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (b). Only the topmost quintuple layer is shown. Small (red) and medium sized (blue) spheres represent Se and Bi atoms, respectively. In (a) Cs occupies the topmost layer Se site and is located at a vertical height of $d_{\perp }=1.2\AA$ above the Se layer while in (b) Cs is located in the $fcc$ hollow site, at 2.1 Å. Interatomic distances are given in Ångström units. Changes of the vertical interlayer spacings relative to the bulk values within the topmost QL are listed on the right.

Figure 3

Contour plot of the unweighted residuum $R_u$ versus the occupancies of the surface substitutional site ${\mathrm{\Theta }}_{\mathrm{sub}}$ and the vdW site ${\mathrm{\Theta }}_{vdW}$. The minimum is at ${\mathrm{\Theta }}_{\mathrm{sub}}\approx 0.45$, while ${\mathrm{\Theta }}_{vdW}$ approximately equals to 0.

Figure 4

(a)–(d): Experimental (symbols) and calculated (lines) intensities for about 0.8 ML of Cs atoms deposited on MBE grown ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) at room temperature. (e): Plot of $|{\mathrm{F}}_{\mathrm{obs}}|$ versus $|{\mathrm{F}}_{\mathrm{calc}}|$ for all 228 symmetry independent reflections. The diagonal line represents the ideal condition $|{\mathrm{F}}_{\mathrm{calc}}|=|{\mathrm{F}}_{\mathrm{obs}}|$. (f): Schematic view of the ${\mathrm{a}}^{☆}-{\mathrm{b}}^{☆}$ plane of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) reciprocal lattice emphasizing the symmetrical independent section.

Figure 5

(a) $400\times 400{\mathrm{nm}}^2$ overview STM image ($U=-1.0\mathrm{V}$, $I=500\mathrm{pA}$) of $\mathrm{Cs}/{\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001). Initial adsorption of Cs leads to the formation of one-dimensional-like structures along the upper step edges of the substrate crystal. Some islands are also observed to adsorb on the terraces. (b) Atomic resolution image ($U=-1.0\mathrm{V}$, $I=1\mathrm{nA})$ showing bright ($\approx 0.8\AA$) protrusions in registry with surface Se atomic sites. (c) Profile along the line in (b). Protrusions are related to Cs atoms located at Se sites with a maximum apparent elevation of approximately 0.8 Å.

Figure 6

Schematic view of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface containing $\left[0\overline{1}10\right]$-oriented step. Numbers 1–4 in circles indicate the positions of Cs atoms considered to illustrate a Cs chain formation: 1 and $3\left(4\right)—hcp$ ($fcc$) hollows near the step, $2—hcp$ hollow far away from the step. a and b are the vectors of the planar $(1\times 1)$ cell of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface. The green line shows the cut producing $\left[\overline{1}\overline{1}20\right]$-oriented step.

Figure 7

Top views of the cells used for the total energy calculations containing an $fcc$ hollow-site Cs chain (a) and a ${\mathrm{Cs}}_{\text{Se}}$ chain (b) near the same atomic termination of the $\left[0\overline{1}10\right]$-oriented step. The Se vacancies, introduced into the cell shown in (a), are marked by circles and letters “V,” the dashed circle denoting the lateral position of the Se vacancy located at the opposite surface of the 1QL-thick slab (i.e., a Cs free surface of the slab). The right-hand side, which is defect and adatom free, exemplifies another possible atomic termination of the $\left[0\overline{1}10\right]$-oriented step.

Figure 8

Calculated spin-resolved surface band structures of the pristine ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface (a) and that with 0.25 ML of Cs located in the $fcc$ hollow (b) or vacant Se (c) sites. The size of color circles reflects the value and sign of the spin vector Cartesian projections, with red/blue colors corresponding to the positive/negative in-plane components (that directed perpendicular to the k vector), and gold/cyan reflecting the out-of-plane components $+s_z/-s_z$. Green areas correspond to the bulk band structure projected onto the surface Brillouin zone.