Field doping of ${\mathrm{C}}_{60}$ crystals: Polarization and Stark splitting

We investigate the possibility of doping ${\mathrm{C}}_{60}$ crystals by applying a strong electric field. For an accurate description of a ${\mathrm{C}}_{60}$ field-effect device we introduce a multipole expansion of the field, the response of the ${\mathrm{C}}_{60}$ molecules, and the Stark splitting of the molecular levels. The relevant response coefficients and splittings are calculated ab initio for several high symmetry orientations. Using a group theoretic analysis we extend these results to arbitrary orientations of the ${\mathrm{C}}_{60}$ molecules with respect to the external field. We find that, surprisingly, for the highest occupied and the lowest unoccupied molecular orbital, respectively, the two leading multipole components lift the degeneracy of the molecular level in the same way. Moreover the relative signs of the splittings turn out to be such that the splittings add up when the external field induces charge into the respective level. That means that when charge carriers are put into a level, its electronic structure is strongly modified. Therefore, in general, in ${\mathrm{C}}_{60}$ field-effect devices charge is not simply put into otherwise unchanged bands, so already because of this their physics should be quite different from that of the alkali-doped fullerenes.