Polaron properties in 2D organic molecular crystals: directional dependence of non-local electron-phonon coupling

In organic molecular crystals, the polaronic hopping model for the charge transport assumes that the carrier lies at one or a small number of molecules. Such a kind of localization suffers the influence of the non-local electron-phonon (e-ph) interactions associated with intermolecular lattice vibrations. Here, we developed a model Hamiltonian for numerically describing the role played by the intermolecular e-ph interactions on the stationary and dynamical properties of polarons in a two-dimensional array of molecules. We allow three types of electron hopping mechanisms and, consequently, for the nonlocal e-ph interactions: horizontal, vertical, and diagonal. Remarkably, our findings show that the stable polarons are not formed for isotropic arrangements of the intermolecular transfer integrals, regardless of the strengths of the e-ph interactions. Interestingly, the diagonal channel for the e-ph interactions changes the transport mechanism by sharing the polaronic charge between parallel molecular lines in a breather-like mode.