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Theory of metal-intercalated phenacenes: Why molecular valence 3 is special

We develop a correlated-electron minimal model for the normal state of charged phenanthrene ions in the solid state, within the reduced space of the two lowest antibonding molecular orbitals of phenanthrene. Our model is general and can be easily extended to study the normal states of other polycyclic aromatic hydrocarbon superconductors. The main difference between our approach and previous correlated-electron theories of phenacenes is that our calculations are exact within the reduced basis space, albeit for finite clusters. The enhanced exchange of electron populations between these molecular orbitals, driven by Coulomb interactions over and above the bandwidth effects, gives a theoretical description of the phenanthrene trianions that is very different from previous predictions. Exact many-body finite cluster calculations show that while the systems with molecular charges of $-$1 and $-$2 are one- and two-band Mott-Hubbard semiconductors, respectively, molecular charge $-$3 gives two nearly $\frac{3}{4}$-filled bands, rather than a completely filled lower band and a $\frac{1}{2}$-filled upper band. The carrier density per active molecular orbital is thus nearly the same in the normal state of the superconducting aromatics and organic charge-transfer solids, and may be the key to understanding unconventional superconductivity in these molecular superconductors.