Electron-phonon coupling in potassium-doped superconducting picene

We explore the properties of electron-phonon couplings in K$_3$Picene, in the framework of density functional theory (DFT). By exploiting the maximally localized Wannier function formalism, we identify the contribution of the intra- and intermolecular phonon vibrations and the role of local and non-local electronic states in determining the electron-phonon coupling. Despite the molecular nature of the crystal, we find that the purely molecular contributions account for only 20{\%} of the total electron-phonon interaction $\lambda $. In particular, the Holstein-like contribution to $\lambda $ are four times smaller than those computed for an isolated neutral molecule, as they are strongly screened by the metallic bands of the doped crystal. The major contribution (80{\%}) to $\lambda $ in K$_3$Picene comes from non-local couplings due to phonon modulated hoppings. We show that the crystal geometry together with the molecular picene structure leads to a strong 1D spatial anisotropy of the non-local couplings. Finally, we propose a lattice model of the electron-phonon couplings in K3Picene that gives 90{\%} of the $\lambda $ obtained in first principles calculations [1]. \\[4pt] [1] M. Casula, M. Calandra and F. Mauri, PRL 107, 137006 (2011), PRB 86, 075445 (2012)