Energetics and electronic structures of potassium-intercalated ${\mathrm{C}}_{60}$ peapods

Total-energy electronic-structure calculations were performed to explore energetics and electronic structures of a one-dimensional array of ${\mathrm{C}}_{60}$ and potassium atoms encapsulated in metallic nanotubes. We find that the electron states of the potassium intercalated peapods depend on the number of potassium atoms intercalated. Intercalation induces substantial hybridization between $\pi$ electron states of ${\mathrm{C}}_{60}$ and the nanotube. The local density of states around the Fermi level shows that the potassium intercalated ${\mathrm{C}}_{60}$-peapod is a novel metal whose carriers are distributed on both the ${\mathrm{C}}_{60}$ and the nanotube.

Figure 1

(Color online) Top and side views of geometric structures of potassium intercalated ${\mathrm{C}}_{60}$-peapods, (a) ${\mathrm{K}}_1{\mathrm{C}}_{60}$, (b) ${\mathrm{K}}_2{\mathrm{C}}_{60}$, (c) ${\mathrm{K}}_3{\mathrm{C}}_{60}$, (d) ${\mathrm{K}}_4{\mathrm{C}}_{60}$, (e) ${\mathrm{K}}_6{\mathrm{C}}_{60}$, and (f) ${\mathrm{K}}_8{\mathrm{C}}_{60}$. Gray (red) circles denote carbon and potassium atoms, respectively.

Figure 2

Reaction energies $\Delta E$ (see text) in the intercalation reaction of the potassium atoms for the ${\mathrm{C}}_{60}$ chain encapsulated in (10, 10) nanotube.

Figure 3

(Color online) Electronic structures of potassium intercalated ${\mathrm{C}}_{60}$-peapods, (a) ${\mathrm{K}}_1{\mathrm{C}}_{60}$, (b) ${\mathrm{K}}_2{\mathrm{C}}_{60}$, (c) ${\mathrm{K}}_3{\mathrm{C}}_{60}$, (d) ${\mathrm{K}}_4{\mathrm{C}}_{60}$, (e) ${\mathrm{K}}_6{\mathrm{C}}_{60}$, and (f) ${\mathrm{K}}_8{\mathrm{C}}_{60}$. Right and left panels of each figure are the electronic energy band and density of states (DOS), respectively. Energies are measured from the Fermi level energy $E_F$. Dotted vertical lines denote the Fermi level energy.

Figure 4

Contour plots of the squared wave function at the $\Gamma$ point of the $t_{1u}$-like states of ${\mathrm{K}}_3{\mathrm{C}}_{60}$-peapod. (a) The lowest, (b) the second lowest, and (c) the highest branches of the $t_{1u}$-like states. Each contour represents the twice (or half) of the density of the adjacent contour lines. The lowest values represented by the contour is $1.562\times {10}^{-4}e∕{\left(\mathrm{a.u.}\right)}^3$. The dotted circle and lines denote the atomic positions of ${\mathrm{C}}_{60}$ and nanotube, respectively.

Figure 5

Contour plots of the local density of states near the Fermi level $\left({\rho }_{E_F}\left(\mathbf{r}\right)\right)$ of the ${\mathrm{K}}_x{\mathrm{C}}_{60}$-peapods, (a) ${\mathrm{K}}_1{\mathrm{C}}_{60}$, (b) ${\mathrm{K}}_2{\mathrm{C}}_{60}$, (c) ${\mathrm{K}}_3{\mathrm{C}}_{60}$, (d) ${\mathrm{K}}_4{\mathrm{C}}_{60}$, (e) ${\mathrm{K}}_6{\mathrm{C}}_{60}$, and (f) ${\mathrm{K}}_8{\mathrm{C}}_{60}$. Each contour represents the twice (or half) of the density of the adjacent contour lines. The lowest values represented by the contour is $6.25\times {10}^{-4}e∕{\left(\mathrm{a.u.}\right)}^3$. The dotted circle and lines denote the atomic positions of ${\mathrm{C}}_{60}$ and nanotube, respectively.