Signatures of an atomic crystal in the band structure of a ${\mathrm{C}}_{60}$ thin film

Transport phenomena in molecular materials are intrinsically linked to the orbital character and the degree of localization of the valence states. Here we combine angle-resolved photoemission with photoemission tomography to determine the spatial distribution of all molecular states of the valence band structure of a ${\mathrm{C}}_{60}$ thin film. While the two most frontier valence states exhibit a strong band dispersion, the states at larger binding energies are characterized by distinct emission patterns in energy and momentum space. Our findings demonstrate the formation of an atomic crystal-like band structure in a molecular solid with delocalized $\pi$-like valence states and strongly localized $\sigma$ states at larger binding energies.

Figure 1

(a) Energy vs momentum cut through the ARPES data along the $\overline{\mathrm{\Gamma }}\overline{M}{\overline{\mathrm{\Gamma }}}^{\prime }$ direction of the surface Brillouin zone for a crystalline ${\mathrm{C}}_{60}$ thin film (5 ML, $E_{\mathrm{photon}}=35$ eV, $p$-polarized light). The surface Brillouin zone is shown in the lower panel together with the intensity scale of the ARPES data. (b) PT simulation of the same energy vs momentum cut based on a DFT calculation of a free-standing ${\mathrm{C}}_{60}$ layer. (c) Density of states projected onto the $\pi$ and $\sigma$ states of ${\mathrm{C}}_{60}$. For comparison, the spectral density of the total photoemission yield is included as a gray curve.

Figure 2

(a) Constant energy (CE) maps extracted from the ARPES data cube in the binding energy region of the HOMO-1 band at $E_{\mathrm{B}}=2.9$ eV and $E_{\mathrm{B}}=3.5$ eV. The corresponding CE maps predicted by our photoemission tomography simulation (PT) are shown in (b) for identical binding energies.

Figure 3

Energy vs momentum cut of the HOMO-1 bands of a ${\mathrm{C}}_{60}$ thin film recorded with vertical (a) and horizontal (b) light polarization $(E_{\mathrm{photon}}=35$ eV). The contrast of both energy vs momentum cuts is enhanced by using the second derivative of the experimental data. The left half of (c) shows the PT simulation of the energy vs momentum cut in the first Brillouin zone, the right half the band structure of our density functional theory calculation. The red and blue solid lines are tight-binding simulations to describe the experimental band dispersion observed for $p$- (blue) and $s$-polarized light (red). (d) Real-space partial charge density distributions of the HOMO and HOMO-1 bands integrated in energy windows from 1.5 to 2.5 eV and 2.75 to 4.0 eV for the HOMO and HOMO-1 respectively. The partial charge density plots are shown in a top view of the ${\mathrm{C}}_{60}$ unit cell in a plane through the center of the ${\mathrm{C}}_{60}$ molecules.

Figure 4

(a) Experimentally determined CE maps at three selected energies from left to right: 8.7, 7.9, and 7.4 eV. The corresponding PT simulations are shown in (b). Note that the CE maps in the PT simulations were extracted at slightly different binding energies as the experimental data. This is due to an energy difference in the initial state energy in our experiment and in the DFT calculations. (c) Partial charge density in real space of a $\sigma$ state integrated in energy windows from 6.0 to 6.5 eV.