Strong Intramolecular Electron-Phonon Coupling in the Negatively Charged Aromatic Superconductor Picene

Superconductivity was recently discovered in solid potassium-intercalated picene (${\mathrm{K}}_{3}22\mathrm{ph}$), in which the picene molecule becomes trianionic ($22{\mathrm{ph}}^{3-}$). In this Letter, we conduct a theory-based study of the superconductivity of $22{\mathrm{ph}}^{3-}$ within the framework of BCS theory. We estimate the density of states $N({\epsilon }_F)$ on the Fermi level to be 2.2 states per (eV molecule spin) by using the theoretical intramolecular electron-phonon coupling $l_x$ and the experimental superconducting transition temperature $T_c$ of 18 K. The theoretical value is consistent with the 1.2 states per (eV molecule spin) determined experimentally for ${\mathrm{K}}_{3}22\mathrm{ph}$ with $T_c=18\mathrm{K}$, indicating the validity of our theoretical treatment and the electron-phonon mechanism for superconductivity. The predicted $l_x$, 0.206 eV, for $22{\mathrm{ph}}^{3-}$ is larger than any value reported for organic superconductors, so picene may have the largest $l_x$ among the superconductors reported so far.

Figure 1

Schematic representation of hydrocarbon molecules.

Figure 2

(a) Phase patterns of the frontier orbitals and (b) selected vibronically active modes in $22{\mathrm{ph}}^{2-}$; the normal coordinate analyses are performed for $22{\mathrm{ph}}^{2-}$ to determine the electron-phonon coupling interaction of $22{\mathrm{ph}}^{3-}$, as fully described in text and the Supplemental Material [19]. (c) Plots of $l_{x,m}\mathrm{\text{−}}{\nu }_m$ for the tri- and monoanions of 14ph, 18ph, and 22ph. The inverse triangles refer to the $l_{x,m}$ peaks contributing mainly to $l_x$.

Figure 3

Plots of $l_x\mathrm{\text{−}}N$ for tri- and monoanions of polyphenacenes (14ph, 18ph, and 22ph), $(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF})_2{}^{+}$, and $\mathrm{C}_{60}{}^{3-}$. The red and blue squares denote the $l_x$ values for the tri- and monoanions of polyphenacenes, respectively. The green squares denote those for $(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF})_2{}^{+}$ (Ref. 5) and $C_{60}{}^{3-}$ (Refs. 21, 22, 23, 24, 25). In the inset, the $l_x$ values are plotted as a function of $1/N$.