Screening and atomic-scale engineering of the potential at a topological insulator surface

The electrostatic behavior of a prototypical three-dimensional topological insulator, Bi${}_2$Se${}_3$(111), is investigated by a scanning tunneling microscopy (STM) study of the distribution of Rb atoms adsorbed on the surface. The positively charged ions are screened by both free electrons residing in the topological surface state as well as band bending induced quantum well states of the conduction band, leading to a surprisingly short screening length. Combining a theoretical description of the potential energy with STM-based atomic manipulation, we demonstrate the ability to create tailored electronic potential landscapes on topological surfaces with atomic-scale control.

Figure 1

STM topographs of Rb single atoms on stoichiometric and Ca-doped Bi${}_2$Se${}_3$ (30 nm $\times$ 30 nm). (a) Stoichiometric Bi${}_2$Se${}_3$ with a 1.2% ML coverage of Rb. The inset indicates a cross section along the line in (a) that depicts the apparent heights of a Se vacancy and two Rb atoms. (b) Ca-doped Bi${}_2$Se${}_3$ with 2.0% ML Rb. (c) Stoichiometric Bi${}_2$Se${}_3$ with 5.8% ML Rb. (d) Stoichiometric Bi${}_2$Se${}_3$ with 6.9% ML Rb. The small hexagon depicts the $(\sqrt{12}\times \sqrt{12})R{30}^{\circ }$ superstructure. Insets in (b)–(d): autocorrelation plots of the atoms' positions (5 nm $\times$ 5 nm, each vector starts at the center. The number of the individual counts is plotted logarithmically using the depicted color scale).

Figure 2

(a) STM topograph of Rb adatoms on an intrinsic Bi${}_2$Se${}_3$ sample, with atomic resolution of the substrate lattice. (b) Top view on three unit cells of the Bi${}_2$Se${}_3$(111) surface, cleaved along the van der Waals gap. The surface Se atoms are colored red, the subsurface Bi atoms are blue, and the second subsurface Se atoms are yellow.

Figure 3

(a) The counts, represented by height, from the autocorrelation images are indexed into colored hexagonal cells labeled by $(j,k)$, shown here for the coverage in Fig. 1. (b) Same procedure for a randomly generated distribution with the same coverage. (c) Distribution functions $f\left(r\right)$ and $f_{\mathrm{ran}}\left(r\right)$ extracted from (a) and (b), respectively, after averaging over all $k$ values for a given $j$. Each hexagonal cell $j$ is color-coded in (a) and (b) as indicated above the graph.

Figure 4

(a) Reduced pair potential, $v\left(r\right)/k_{\mathrm{B}}T$, for various Rb coverages and for stoichiometric and Ca-doped Bi${}_2$Se${}_3$. The lines connect points at a given coverage as a guide to the eye. The dashed lines mark regions where $v\left(r\right)/k_{\mathrm{B}}T$ is affected by a limitation of the Percus-Yevick approximation. (b) The experimental data from (a), taking only the data points into account, which are connected by solid lines, are fitted with different unscreened and screened Coulomb potentials, where the shaded regions indicate the error bars (see text).

Figure 5

Tailoring the local potential by surface doping with Rb atoms. (a) Self-assembly of Rb atoms into a superlattice array driven by Coulomb repulsion. (b) Eleven Rb atoms manipulated with the STM tip. The triangles in the center of the “corral” are native subsurface Se vacancies. Manipulation parameters are $I_{\mathrm{T}}=4.6\mathrm{nA}$ and $V_{\mathrm{B}}=600\mathrm{mV}$. (c) Potential landscapes of (b) generated by using $v_2\mathrm{D}\left(r\right)$.

Figure 6

(a) The optimum $v_{\mathrm{PY}}\left(r\right)$ is determined by varying the parameters $({\varepsilon }_{r,\mathrm{PY}}+1)/2$ and ${\lambda }_{\mathrm{PY}}$. For all combinations, squared deviations between the left- and right-hand sides of the Percus-Yevick equation are plotted color-coded. (b) Plot of the coverage-dependent right-hand side of the Percus-Yevick equation that equals $-\Delta w\left(N\right)/k_{\mathrm{B}}T$. The solid line is a fit to a function, which is quadratic in $N$.