Single-particle excitation spectra of ${\mathrm{C}}_{60}$ molecules and monolayers

In this paper, we present calculations of single-particle excitation spectra of neutral and three-electron-doped Hubbard ${\mathrm{C}}_{60}$ molecules and monolayers from large-scale quantum Monte Carlo simulations and cluster perturbation theory. By a comparison with experimental photoemission, inverse photoemission, and angle-resolved photoemission data, we estimate the intermolecular hopping integrals and the ${\mathrm{C}}_{60}$ molecular orientation angle, finding agreement with recent x-ray photoelectron diffraction experiments. Our results demonstrate that a simple effective Hubbard model, with intermediate coupling $U=4t$, provides a reasonable basis for modeling the properties of ${\mathrm{C}}_{60}$ compounds.

Figure 1

(Color online) 2D hexagonal monolayer of identically oriented ${\mathrm{C}}_{60}$ molecules [lattice constant $a=10.02\mathrm{\AA }$ for the superlattice (Ref. 11)] and its corresponding first Brillouin zone. The definition of the molecular rotation angle $\theta$ is the same as in the caption of Fig. 4 of Ref. 11, which is defined by two lines, both projected onto the plane of the layer, one from a molecular center to a NN molecular center, as shown, and the other from a molecular center through a pentagon face center. $\theta =0°$ when these two lines coincide. Counterclockwise rotation of the molecule corresponds to a positive rotation angle. For ${\mathrm{K}}_3{\mathrm{C}}_{60}$, the black squares represent two ${\mathrm{K}}^{+}$ ions, one above the other, while gray ones denote a single ${\mathrm{K}}^{+}$ ion (Ref. 11).

Figure 2

(Color online) DOS of (a) ${\mathrm{C}}_{60}$ and (b) ${\mathrm{C}}_{60}^{3-}$ single molecules from QMC and MEM for $U=4t$ and $\beta t=10$. A total of 465 and 620 bins of space-time Green’s functions are collected for ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{60}^{3-}$, respectively, for MEM analysis. Each bin is an average over 100 space-time Green’s functions, which are collected after each QMC sweep over the whole space-time lattice.

Figure 3

Single-particle spectral functions of a 2D Hubbard model from (a) QMCPT and (b) EDCPT with open boundary conditions. The cluster is of $3\times 4$ dimension. The two methods predict very similar single-particle excitation energies and energy gaps. Note that special $\mathbf{k}$ points $\Gamma$, $M$, and $X$ are for a 2D square lattice, different from those in Fig. 1.

Figure 4

(Color online) DOS of hexagonal (a) ${\mathrm{C}}_{60}$ monolayer with $U=0$, (b) ${\mathrm{C}}_{60}$ monolayer with $U=4t$, and (c) ${\mathrm{K}}_3{\mathrm{C}}_{60}$ monolayer with $U=4t$ from QMCPT calculations for $t^{\prime }=-0.3t$ and $T=0.1t$. Shaded areas are occupied by electrons.

Figure 5

Determination of NN molecular hopping integral $t^{\prime }$ and molecular orientation angle $\theta$ by comparing the experimental ARPES result (Ref. 11) (upper panel) with the theoretical one (lower panel), which has $t^{\prime }=-0.3t$ and molecular rotation angle $\theta =64°$. The energy unit has been converted to eV using $t=2.72\mathrm{eV}$. The momentum unit is ${\mathrm{\AA }}^{-1}$.

Figure 6

(Color online) Comparison of DOS from QMCPT calculations and experimental PES data (Ref. 11) for ${\mathrm{C}}_{60}$ (upper panel) and ${\mathrm{K}}_3{\mathrm{C}}_{60}$ (lower panel) hexagonal monolayers. The QMCPT energy scale has been converted to eV by setting $t=2.72\mathrm{eV}$.

Figure 7

Band dispersions along $\Gamma M$ direction with different rotation angles $\theta$ for a 2D hexagonal ${\mathrm{K}}_3{\mathrm{C}}_{60}$ superlattice from QMCPT calculations. The other parameters are fixed: $U=4t$, $t^{\prime }=-0.3t$, and $T=0.1t$. The momentum unit is ${\mathrm{\AA }}^{-1}$.