Spectral, optical and transport properties of the adiabatic anisotropic Holstein model: Application to slightly doped organic semiconductors

Spectral, optical, and transport properties of an anisotropic three-dimensional Holstein model are studied within the adiabatic approximation. The parameter regime is appropriate for organic semiconductors used in single-crystal-based field-effect transistors. Different approaches have been used to solve the model: the self-consistent Born approximation valid for weak electron-phonon coupling, the coherent potential approximation exact for infinite dimensions, and numerical diagonalization for finite lattices. With increasing temperature, the width of the spectral functions gets larger and larger, making the approximation of a quasiparticle less accurate. On the contrary, their peak positions are never strongly renormalized in comparison with the bare ones. As expected, the density of states is characterized by an exponential tail corresponding to localized states at low temperature. For weak electron-lattice coupling, the optical conductivity follows a Drude behavior, while for intermediate electron-lattice coupling, a temperature-dependent peak is present at low frequency. For high temperatures and low particle densities, the mobility always exhibits a power-law behavior as a function of temperature. With decreasing particle density, at low temperature, the mobility shows a transition from metallic to insulating behavior. Results are discussed in connection with available experimental data.