Intertwined Solitons and Impurities in a Quasi-One-Dimensional Charge-Density-Wave System: $\mathrm{In}/\mathrm{Si}(111)$

Recent studies on a quasi-one-dimensional (quasi-1D) charge-density-wave (CDW) system, In atomic wires on Si(111), have brought intriguing issues on topological solitons in quasi-1D systems: the existence of few-atom-sized solitons, chirality of solitons, and the realization of logic exploiting the chirality switching. Using scanning tunneling microscopy and first-principles calculations, we show that the previously reported “short” phase-flip defects are In adatoms and thus have nonsolitonic nature, resolving the controversy over the existence of highly localized solitons. The observed “long” phase-flip and phase-slip defects are genuine solitons with and without chirality, respectively. While achiral solitons (phase-slip defects) can exist on the pristine CDW ($8\times 2$) surface, chiral solitons (phase-flip defects) cannot due to their breakage of $8\times 2$ ordering. The chiral solitons can exist only when they are trapped by In adatoms and constitute a part of a closed-loop domain wall. The intertwinement of chiral solitons and In adatoms implies the limitations of the previously proposed logic utilizing soliton chirality, but it provides an opportunity to realize this by controlling the In-adatom defect.

Figure 1

STM images of an $\mathrm{In}/\mathrm{Si}(111)$ surface with (a) $4\times 1$ and (b) $8\times 2$ structures taken at 300 K and 80 K, respectively. Both images were obtained with a sample bias voltage ($V_s$) of $-1.5\mathrm{V}$. (c) Schematic illustration of the phase slip and phase flip in a $4\times 2$ wire. The ovals represent CDW features in two possible tilt orientations. (d)–(g) STM images of defects observed on the $8\times 2$ surface, which are classified into two categories: short defects [(d) phase-slip defect (PSD) and (e) phase-flip defect (PFD)] vs long defects [(f) PSD and (g) PFD].

Figure 2

STM images of an $\mathrm{In}/\mathrm{Si}(111)$ surface prepared by a typical recipe [images taken at 300 K ($V_s=-1.5\mathrm{V}$) (a) and at 80 K ($V_s=1.7\mathrm{V}$) (b)]. While the $4\times 1$ surface at 300 K appears perfectly uniform and defect-free, the $8\times 2$ surface at 80 K reveals many bright protrusions (In adatoms). Comparison of the experimental STM image ($V_s=-2.3\mathrm{V}$) of a short PSD (c) and the theoretical simulation ($V_s=-2.2\mathrm{V}$) of an isolated In adatom (d) on an $8\times 2$ surface. Schematic of interwire registries created by an $8\times 2$-preserving short PSD [boxed in (e)] and an $8\times 2$-breaking short PFD [boxed in (f)].

Figure 3

(a) STM image of an $\mathrm{In}/\mathrm{Si}(111)$-($8\times 2$) surface rich with In adatoms taken at 96 K ($V_s=-1.0\mathrm{V}$) and (b) its schematic illustration (In adatoms are designated by red dots). A 2D domain wall (enclosed by lines) consists of In adatoms (short PFDs), chiral solitons (long PFDs), and $4\times 1$ segments. It forms a closed loop and separates topologically two $8\times 2$-CDW domains (I and II). (c) Magnified STM image (top) and its schematic (bottom) of a boxed area, a part of the closed-loop domain wall in (a). The two $8\times 2$ domains (I and II) are separated by phase-flipping segments; chiral solitons [right chiral soliton (RCS) and left chiral soliton (LCS), as designated according to the schemes from Ref. 13], In adatoms (red dots), and $4\times 1$ segments.

Figure 4

(a) Sequential STM images ($V_s=-0.5\mathrm{V}$) and (b) schematic showing temporal motion of a chiral soliton [underlined in the middle wire in (a)] coupled with In adatoms (in the upper and lower wires).

Figure 5

(a) STM image ($V_s=-0.5\mathrm{V}$) of an achiral soliton (long PSD) on an $8\times 2$ surface at 80 K (a full-size image is presented in Fig. S4 [18]). Note that the achiral soliton is well isolated without In adatoms in its vicinity. (b) STM height profile (dots) of the achiral soliton along the white line in (a) together with its best fit by a trial fitting function, $Z(x)=Z_0\tanh [(x-x_0)/\xi ]$ (red and blue lines). Only locally maximal and minimal heights at positions of $n{a}_0$ ($n$: integer) were chosen to remove noises and slowly varying background shapes. The fitting function mimics the soliton as an envelope for the lattice modulation, although the detailed correct functional form is unknown for the soliton in this system. A characteristic length of $\xi =22\pm 2a_0$ was obtained by fitting.