Chiral Single-Wall Gold Nanotubes

Based on first-principles calculations we show that gold atoms can form both freestanding and tip-suspended chiral single-wall nanotubes composed of helical atomic strands. The freestanding, infinite (5,5) tube is found to be energetically the most favorable. While energetically less favorable, the experimentally observed (5,3) tube stretching between two tips corresponds to a local minimum in the string tension. Similarly, the (4,3) tube is predicted as a favorable structure yet to be observed experimentally. Analysis of band structure, charge density, and quantum ballistic conductance suggests that the current on these wires is less chiral than expected, and there is no direct correlation between the numbers of conduction channels and helical strands.

Figure 1

Atomic structure of $(n,m)$ gold SWNTs obtained by cylindrical folding of the 2D triangular lattice. Basis vectors of the 2D lattice are ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$; the chiral vector $\mathbf{C}=n{\mathbf{a}}_1+m{\mathbf{a}}_2$, such that the tube circumference is $|\mathbf{C}|$, and radius $R=(n^2+m^2-nm{)}^{1/2}|{\mathbf{a}}_{\mathbf{1}}|/\mathbf{2}\pi$. An $(n,m)$ tube has $n$ helical strands and $m$ defines the chirality. A dark helical strand of atoms highlights the chirality of the tubes. The radius $R$ and period $L$ are modified upon relaxation of the tubular structure.

Figure 2

Triangles are calculated curvature energy $E_c$ of freestanding SWNT. Dash-dotted curve is the best fit in the form $\alpha /R^2$ ($\alpha =1.19\mathrm{e}\mathrm{V}{\AA }^2$). Diamonds are calculated string tension $f$ of suspended $(n,m)$ gold nanotubes at zero temperature. The local minima of $f$ indicate that (5,3) and (4,3) SWNTs are magic.

Figure 3

Electronic energy-band structure and ballistic conductance of infinite (5,5), (5,3), (4,4), and (4,3) gold SWNTs. The Fermi level is set to zero in each panel. Right panels are contour plots of the total charge density on a plane perpendicular to the tube axis. The charge density is negligible at the centers of the tubes.

Figure 4

Left: Total and orbital-decomposed densities of states around the Fermi level ($E=0$) of (5,3) gold SWNT. Right: A schematic description of the structure, and isosurfaces for the charge densities of the five states at the Fermi level corresponding to current transporting channels c1, c2,…,c5. Three reference points ($A$, $B$, $C$) are shown by dark spots on each plot.