Valence electronic structure of cross-linked ${\mathrm{C}}_{60}$ polymers: In situ high-resolution photoelectron spectroscopic and density-functional studies

When a ${\mathrm{C}}_{60}$ film is irradiated with a $3\mathrm{keV}$ electron beam, a cross-linked ${\mathrm{C}}_{60}$ polymer is formed and exhibits metallic electron-transport $\left(I\text{−}V\right)$ properties in air at room temperature [J. Onoe et al., Appl. Phys. Lett. 82, 595 (2003)]. To elucidate the origin of the metallic $I\text{−}V$ characteristics of the cross-linked polymer, we examined the valence photoelectron spectra of the polymer using in situ high-resolution ultraviolet photoelectron spectroscopy (UPS) and found that the spectrum for the cross-linked ${\mathrm{C}}_{60}$ polymer came across the Fermi level $\left(E_F\right)$. To understand the UPS results for the ${\mathrm{C}}_{60}$ polymer, we performed first-principles calculations of the band structure for three kinds of optimized three-dimensional unit cells of one-dimensional (1D) cross-linked ${\mathrm{C}}_{60}$ polymers with a cross-linkage consisting of both six- and seven-membered rings and of five- and eight-membered rings (P58). It was found that one quasi-1D P58 cross-linked ${\mathrm{C}}_{60}$ polymer shows semimetallic properties, which provides one possible explanation of both previous (metallic $I\text{−}V$ characteristics) and present (valence photoelectron spectra) experimental results.

Figure 1

(Color) In situ high-resolution UPS spectra of pristine ${\mathrm{C}}_{60}$ film (blue line) and cross-linked ${\mathrm{C}}_{60}$ polymer (red line) obtained at 300 and $350\mathrm{K}$, respectively. The inset shows the UPS spectrum of the cross-linked ${\mathrm{C}}_{60}$ polymer near the Fermi level.

Figure 2

(Color online) Schematic representation of the three optimized quasi-one-dimensional unit cells of the cross-linked ${\mathrm{C}}_{60}$ polymer with a cross-linkage consisting of both six- and seven-membered rings (abbreviated as P67) and of five- and eight-membered rings (abbreviated as P58). Geometry of monoclinic (hexagonal) unit cell ($a\sim b\sim c$, $\alpha =\beta =90°$, and $\gamma =60°$ and 60.5° for P67 and P58, respectively) in which P67 or P58 is placed parallel to one of the hexagonal axes.

Figure 3

(Color online) First-principles calculated results of the energy band structure for P67 and P58 ${\mathrm{C}}_{60}$ polymers with the unit cell as shown in Fig. 2. The inset shows schematic representation of the $[2+2]$ dumbbell bond formed between adjacent 1D P58 cross-linked ${\mathrm{C}}_{60}$ polymers, which corresponds to the cross-point in $k$ space between the HOMO and LUMO bands.