Sub-Poissonian distribution of Cs and K ions in the valleys of hBN/Ru(0001)

The moiré pattern of hBN/Ru(0001) provides a template for the adsorption of the alkali metals Cs and K: Scanning tunneling microscopy reveals that the adatoms prefer to adsorb in the valley areas of the moiré unit cell. Distinctive from transition metal adatoms that tend to agglomerate, the alkali metal adatoms avoid each other within the valleys, leading to a sharper distribution than the Poisson statistics expected for noninteracting particles. This sub-Poissonian distribution is further explored via Monte Carlo simulations. The average charge $q$ of the alkali metal adatoms is extracted for different alkali metal concentrations $\lambda$, which reveals a monotonically decreasing $q\left(\lambda \right)$ dependence. We explain this dependence with the energy trade-off between the charge transfer from the alkali metals to the more electron-affine Ru(0001) substrate and the static electric field created by this charge transfer.

Figure 1

(a) and (b) STM images of hBN/Ru(0001) with Cs adsorption. Cs concentration is $\lambda =$ 1.11 ${\mathrm{MUC}}^{-1}$ (a) and $\lambda =3.19{\mathrm{MUC}}^{-1}$ (b). Image size is $25.6\times 25.6{\mathrm{nm}}^2$. Bias voltage is $U_{\text{b}}=-2.0\mathrm{V}$ (a) and $U_{\text{b}}=-2.4\mathrm{V}$ (b). Tunneling current is $I_{\text{t}}=20$ pA. (c) Cs density dependence on the distance to the cell center obtained from over a hundred singly occupied cells for $\lambda =$ 1.11 ${\mathrm{MUC}}^{-1}$.

Figure 2

Occupation number $n$ distribution for (a) Cs and (b) K. Experimental observation, black circles; Poisson distribution, gray symbols (areas to guide the eye); MC simulation, red symbols (lines to guide the eye).

Figure 3

(a) Simulated AM atom geometries in the potential well with $n=1\text{−}5$, and some of the valleys of the correspondent $n$ AM adatoms forming the expected regular polygon geometries imaged by STM. (b) Energy $E_n$ of a potential well confining $n$ adatoms. (c) Optimized charge $q$ (in units of the elementary charge $e_0$) plotted against the correspondent AM concentration as black (Cs) and blue (K) circles. The vertical error bars of the first four data points and the error bars that are smaller than the data point circles are left out. The blue (K) and black (Cs) curves present the optimized fit to Eq. (9).