Conductivity mechanisms in phthalocyanine-based "molecular metals": Calculation of the temperature-dependent resistivity

The temperature dependence of the conductivity σ in the low-dimensional material, NiPcI (Pc = phthalocyanine), is investigated using a transport theory for noninteracting electrons in a tight-binding band scattered by one- and two-phonon processes. The lattice motions found to be the dominant sources of resistivity along the chain are the longitudinal stretch and the interplanar twist (libron), with the former being a first-order scattering process (σ_1p ∝ l/T) and the latter a second-order mechanism (σ_2l ∝ 1/T²). The resulting conductivity has a room-temperature value of ∼400 Ω^-1 cm^-1 which increases to almost 4000 Ω^-1 cm ^-1 at 50 K, with an overall temperature dependence of σ∼ T^-1.4, in good agreement with experiment. It is found that at low temperature, one-phonon scattering is most important, while at room temperature one-phonon and two-libron scattering contribute nearly equally to the resistivity. The accuracy of the bandwidths and of the electron/phonon coupling constants, calculated using first-principles electronic structure methods, shows the value of these techniques for studying conduction in "molecular metals", while the good agreement of our calculated resistivity plots with those measured experimentally both supports the straightforward narrow-band picture used for the conduction process, and provides valuable insights into the design of optimal molecular metals of this class.