Ab initio study of helical silver single-wall nanotubes and nanowires

We report results for the electronic structures of extended silver single-wall nanotubes (AgSWNTs) within a first-principles, all-electron self-consistent local density functional approach adapted for helical symmetry. We carried out calculations on twenty-one different AgSWNTs ranging in radii from approximately $1.3\mathrm{\AA }$ to $3.6\mathrm{\AA }$. AgSWNTs with radii greater than $2.2\mathrm{\AA }$ were also calculated with a silver atomic chain inserted along the nanotube axis; we refer to these composite structures as silver nanowires (AgNWs). Energetic trends for the AgSWNTs are not as predictable as expected. For example, the total energy does not necessarily decrease monotonically as nanotube radius increases, as is the case for single-wall carbon nanotubes. The conductivity of these AgSWNTs and AgNWs is also addressed. Similar to the case for helical gold nanowires, the number of conduction channels in the AgSWNTs does not always correspond to the number of atom rows comprising the nanotube. However, for all AgNWs considered, the additional silver atomic chain placed along the tube’s axis results in one additional conduction channel.

Figure 1

Triangular network of silver (or gold) atoms. Basis vectors are designated as ${\mathit{a}}_1$ and ${\mathit{a}}_2$. Each tube is labeled by two integers $(n_1,n_2)$, where the rollup vector is $\mathit{R}=n_1{\mathit{a}}_1+n_2{\mathit{a}}_2$. The dashed lines represent lines of symmetry; an irreducible wedge is formed between the lines $n_1=n_2$ and $n_1=2n_2$. AgSWNTs labeled with a solid marker correspond to the nanotubes that we consider in the present study. AgSWNTs located to the right of the bold line, ranging from (5,5) to (8,4), were also modeled with a silver atomic chain inserted along the axis of the nanotube. AgSWNTs containing an axial chain are designated as nanowires (AgNWs).

Figure 2

Models of selected AgSWNTs and the (7,5) AgNW (AgSWNT + inserted silver atomic chain).

Figure 3

Total energy per silver atom versus nanotube radius. Open circles represent AgSWNTs and closed circles represent AgNWs. The (7,5) AgNW has the lowest energy and is centered about zero; the energies of all other tubes are plotted with respect to zero. Local minima in total energy are shown for the (4,2), (5,3), (6,3), (7,4), (7,5), (8,5), and (8,7) AgSWNTs.

Figure 4

Total energy per silver atom versus nanotube radius for all (a) “$n_1=n_2$” type and (b) “$n_1=n_2+1$” type AgSWNTs. The solid line represents calculated values, while the dashed line represents a $1∕R^2$ fit. In each case, the calculated values fall off at a rate faster than $1∕R^2$. Calculated values are given in Table .

Figure 5

Band structures for the (a) (7,4) AgSWNT, (b) silver atomic chain, and (c) the (7,4) AgNW. Fermi levels are shown with a dashed line. Points correspond to the orbital density images shown in Fig. 6. The band crossing the Fermi level in (b), shown in bold, is shifted higher in energy into the conduction band in (c). The band that lies just above the Fermi level in the AgSWNT shown in (a) dips below the Fermi level upon inserting the chain as shown in (c). Inserting the chain lowers the energies of the bands from the AgSWNT with respect to the Fermi level, resulting in one additional conduction channel. The number of Fermi crossings corresponds to the number of conduction channels in a particular structure. There are five Fermi crossings in (a), one Fermi crossing in (b), and six Fermi crossings in (c).

Figure 6

(Color online) Orbital densities for the (a) (7,4) AgSWNT, (b) silver atomic chain, and (c) (7,4) AgNW. The structure of the inserted chain (c) is shown in red to aid in visualization. The images correspond to bands at specific points within the Brillioun zone, as indicated in Fig. 5 by solid dots. The numbering scheme from 1 to 6 corresponds to the solid dots located from left to right, respectively.