2D bands and electron-phonon interactions in polyacene plastic transistors

We present a simple tight-binding model for the two-dimensional energy bands of polyacene field-effect transistors and for the coupling of these bands to lattice vibrations of their host molecular crystal. We argue that the strongest electron-phonon interactions in these systems originate from the dependence of inter-molecule hopping amplitudes on collective molecular motion, and introduce a generalized Su-Schrieffer-Heeger model that accounts for all vibrations and is parameter-free once the band mass has been specified. We compute the electron-phonon spectral function ${\alpha }^{2}F(\omega )$ as a function of two-dimensional hole density, and are able to explain the onset of superconductivity near 2D carrier density $n_{2D}\sim {10}^{14}c{m}^{-2}$, discovered in recent experiments by Sch"on {\it et al.} \onlinecite{Batlogg}.