Electron-Phonon Coupling in Crystalline Organic Semiconductors: Microscopic Evidence for Nonpolaronic Charge Carriers

We consider electron-phonon coupling in crystalline organic semiconductors, using naphthalene for our case study. Employing a first-principles approach, we compute the changes in the selfconsistent Kohn-Sham potential corresponding to different phonon modes and go on to obtain the carrier-phonon coupling matrix elements (vertex functions). We then evaluate perturbatively the quasiparticle spectral residues for electrons at the bottom of the lowest unoccupied (LUMO), and holes at the top of the highest occupied (HOMO), band, obtaining $Z_{\mathrm{e}}\approx 0.74$ and $Z_{\mathrm{h}}\approx 0.78$, respectively. Along with the widely accepted notion that the carrier-phonon coupling strengths in polyacenes decrease with increasing molecular size, our results provide strong microscopic evidence for the previously conjectured nonpolaronic nature of bandlike carriers in these systems.

Figure 1

(a) An illustration of the crystal structure of naphthalene, comprising molecular layers (in the $a-b$ plane) stacked in the crystallographic $c$ direction. Each unit cell contains two inequivalent naphthalene molecules in a herringbone-like arrangement. (b) The irreducible wedge of the Brillouin zone in the naphthalene crystal. The zone center ($\Gamma$-point) is indicated, along with the reciprocal basis vectors.

Figure 2

Calculated phonon-momentum dependence of the moduli of the $e$-ph vertex functions in the $a-b$ plane for (a) electrons at the bottom of the LUMO band, and (b) holes at the top of the HOMO band, interacting with phonons of the lowest optical branch (the zone-center energy is 11.4 meV).

Figure 3

Upper panel: Contributions of different phonon modes, divided into 20 meV-wide energy intervals, to the quasiparticle renormalization for electrons and holes. Lower panel: Phonon density-of-states (DOS).

Figure 4

The temperature dependence of inelastic scattering rates for bandlike electron and hole states in naphthalene.