Magic Structures and Quantum Conductance of $[110]$ Silver Nanowires

We investigate the pathway of thinning process for transient $[110]$ nanowires (NWs) of Ag. The result is in good agreement with experimental observations. An unambiguous identification of the structure of a NW requires at least two views along different directions. In the cases where two views of different NW structures are practically the same for very thin NWs which pose experimental difficulty due to small signal-to-noise ratio, our theoretical analysis helps distinguish these structures. On the basis of conductance ($G$) calculations vis-á-vis the structure of transient NWs, the puzzling experimental observation of fractionally quantized $G$ values is explained by considering the existence of mixed structures for thin wires.

Figure 1

Energy vs $\sqrt{(N/L)}$ (or effective radius, $R$) (a) and tension vs $\sqrt{(N/L)}$ of $[110]$ Ag NWs (b). The top view (the cross section of NW along $[110]$) followed by two side views (along $[-110]$ and $[001]$) is shown for the well-favored (except $4/2$ and $2/1$) structures. The unlabeled structures (from bottom to top) are $4/1$, $3/4$, $6/2$, $2/6$, $6/4$, $8/3$, $6/6$, $5/8$, $8/5$, and $15/8$.

Figure 2

Simplified picture representing the extraction of a NW from bulk.

Figure 3

Pathway (showing up the top view) of the thinning process for $[110]$ Ag NWs. The value in parentheses are the energy per atom in eV.

Figure 4

(a) Example of mixed structure. The $4/3\times 3-2/2\times 3$ structure as device part is located between both leads comprised of $5/4\times 4$ structures (b) Change of conductance during the evolution of each structure, $4/3\times L$ ($L=1\sim 8$), $4/3\times 3-2/2\times M$ ($M=1\sim 4$) and $4/3\times 3-2/2\times 2-1/1\times N$ ($N=1\sim 3$), between two $5/4$ leads or between two infinite planar surfaces (110). Indices $L$, $M$, and $N$ denote the units of each structure during evolution as in (a). (c)–(e) Transmission vs energy curves for $[110]$ NWs for pure and mixed structures. Shortened labels are used; e.g., $5/4-4/3$ means that both lead parts have $5/4$ structure and the central part has $4/3$ structure.