Broken Even-Odd Symmetry in Self-Selection of Distances between Nanoclusters due to the Presence or Absence of Topological Solitons

Depositing particles randomly on a 1D lattice is expected to result in an equal number of particle pairs separated by even or odd lattice units. Unexpectedly, the even-odd symmetry is broken in the self-selection of distances between indium magic-number clusters on a $\mathrm{Si}(100)\mathrm{\text{−}}2\times 1$ reconstructed surface. Cluster pairs separated by even units are less abundant because they are linked by silicon atomic chains carrying topological solitons, which induce local strain and create localized electronic states with higher energy. Our findings reveal a unique particle-particle interaction mediated by the presence or absence of topological solitons on alternate lattices.

Figure 1

(a) Room temperature STM images (taken at sample bias of $-2.1\mathrm{V}$) of In-SMCs (bright spots) on a $\mathrm{Si}(100)\mathrm{\text{−}}2\times 1$ surface. (b) An In-SMC at one end of two Si-dimer chains. (c) $D_n$-cluster pairs with $n=1–8$.

Figure 2

(a) Experimental histogram of $D_n$-cluster pairs. The gray line is a histogram derived from Monte Carlo simulation of cluster deposition. (b) Red symbols are second derivative of the populations $N_n$ of $D_n$-cluster pairs. Yellow symbols are second derivative of the calculated energy $E_n$ of a system containing a $D_n$-cluster pair.

Figure 3

(a) Top-view schematic of an atomic model of $D_{10}$-cluster pairs, with two topological solitons located at the centers of chains. Inset shows top 8 most distorted Si-Si bonds, marked by green sticks, around topological solitons. (b) Simulated STM image corresponding to (a). (c) Observed STM image at room temperature. (d) Simulated STM image corresponding to (c).

Figure 4

(a) Low temperature (110 K) STM image shows frozen topological solitons, as marked by $S1$ and $S2$, on two Si-dimer chains of a $D_{10}$-cluster pair. (b) Simulated STM image corresponding to (a). (c) Calculated energy of a $D_{10}$-cluster pair as function of the locations of two topological solitons.

Figure 5

(a) and (b) Projected charge density distributions of electronic states near HOMO for $D_{11}$- and $D_{12}$-cluster pair, respectively. Energies (eV) of these states with respects to HOMO are labeled beside the panels. (c) Energies of LUMO and HOMO-2 states of $D_n$-cluster pairs.