Intercalant and Intermolecular Phonon Assisted Superconductivity in K-Doped Picene

${\mathrm{K}}_3$ picene is a superconducting molecular crystal with a critical temperature of $T_c=7$ or 18 K, depending on the preparation conditions. Using density functional theory we show that electron-phonon interaction accounts for $T_c$ 3–8 K. The average electron-phonon coupling, calculated by including the phonon energy scale in the electron-phonon scattering, is $\lambda =0.73$ and ${\omega }_{\log }=18.0\mathrm{meV}$. Intercalant and intermolecular phonon modes contribute substantially (40%) to $\lambda$ as also shown by the isotope exponents of potassium (0.19) and carbon (0.31). The relevance of these modes makes superconductivity in K-doped picene peculiar and different from that of fullerenes.

Figure 1

DFT-LDA band structure of ${\mathrm{K}}_3{\mathrm{C}}_{22}{\mathrm{H}}_{14}$ near the Fermi level. The DOS per spin per cell (comprising two picene molecules) is shown in the right-hand panel. Note the strong DOS variation in a range of $\pm \hslash {\omega }_{\log }$ from the Fermi energy, with the characteristic phonon frequency ${\omega }_{\log }=18\mathrm{meV}$.

Figure 2

(c),(d) Phonon DOS of ${\mathrm{K}}_3{\mathrm{C}}_{22}{\mathrm{H}}_{14}$ crystal and picene molecule, respectively. The DOS is projected on phonon subspaces $S$ which correspond to hydrogen (H), potassium (K), out-of-plane and in-plane carbon (${\mathrm{C}}_{\perp }$ and ${\mathrm{C}}_{=}$) modes. The black solid curve is the sum of K and intermolecular modes. In (d) the black line is absent as there is no K and all phonons are intramolecular, except for the six rototranslational modes at zero frequency. We do not show the C-H stretching modes, which do not couple to electrons and are located around $3050{\mathrm{cm}}^{-1}$, well above the frequency range plotted. (a),(b) $\lambda (\omega )$ and ${\alpha }^{2}F(\omega )$ resolved by projections on H, K, ${\mathrm{C}}_{\perp }$, and ${\mathrm{C}}_{=}$ phonons. $\lambda (\omega )$ ramps up by 90% in the first $300{\mathrm{cm}}^{-1}$. The black solid line is the sum of K and intermolecular modes, which contribute to 40% of the total $\lambda$.