Strong correlation effects in the fullerene ${\mathrm{C}}_{20}$ studied using a one-band Hubbard model

The smallest fullerene, dodecahedral ${\mathrm{C}}_{20}$, is studied using a one-band Hubbard model parametrized by $U∕t$. Results are obtained using exact diagonalization of matrices with linear dimensions as large as $5.7\times {10}^9$, supplemented by quantum Monte Carlo. We report the magnetic and spectral properties of ${\mathrm{C}}_{20}$ as a function of $U∕t$ and investigate electronic pair binding. Solid forms of ${\mathrm{C}}_{20}$ are studied using cluster perturbation theory, and evidence is found for a metal-insulator transition at $U\sim 4t$. We also investigate the relevance of strong correlations to the Jahn-Teller effect in ${\mathrm{C}}_{20}$.

Figure 1

(Color online) (a) HMO levels for neutral ${\mathrm{C}}_{20}$ with $I_h$ symmetry. (b) The Walsh diagram showing the evolution of the levels with the distortion $ϵ$ toward $D_{3d}$ symmetry. (c) HMO levels for the molecule with $D_{3d}$ symmetry $(ϵ=1)$.

Figure 2

(Color online) Electronic pair binding energy ${\Delta }_b\left(21\right)∕t$ as a function of $U∕t$. ED (●) and QMC (엯) results for the molecule with $I_h$ symmetry. ED results (▴) for the molecule with $D_{3d}$ $(\epsilon =1)$ symmetry. The solid (crossed) vertical line indicates $U_c∕t$ for neutral $I_h$ $\left(D_{3d}\right)$ molecules. (a) ${\Delta }_b$ versus $U∕t$ for $U∕t⩽5$. (b) ${\Delta }_b$ versus $t∕U$ for $5⩽U∕t⩽100$.

Figure 3

(Color online) Shift in the ground-state energy of the neutral molecule, $\Delta E$, versus the distortion $\epsilon$. The Jahn-Teller instability is quite pronounced for $U∕t=2$ (엯), but it is essentially absent for $U∕t=8$ (●).

Figure 4

(Color online) Density of states $N\left(\omega \right)$ at (a) $U=2t$ from QMC and at (b) $U=5t$ from ED. In both panels, the density of states for the ${\mathrm{C}}_{22}$ fcc lattice obtained from CPT with $t^{\prime }=-t$ is shown as a dashed line.

Figure 5

Spectral functions with the chemical potential $\mu$ determined from $N\left(\omega \right)$ in Fig. 4. Results for the ${\mathrm{C}}_{22}$ fcc lattice with (a) $U=2t$ and (b) $U=5t$ as obtained from CPT with $t^{\prime }=-t$. The $k$-axis labels refer to standard notation for the FCC Brillouin zone.