Temperature trends of carrier transport in doped conjugated polymers

Charge transport in conjugated polymers (CPs) typically thought to be phonon-assisted carrier hopping between localized or partly delocalized sites. The hopping model predicts a monotonic increase of the conductivity σ with temperature. However, measurements of conductivity in CPs show several distinct dependences. For some CPs, σ increases with T, consistent with phonon-assisted hopping, while for others it decreases or shows a doping-dependent peak. Here we show that electron-phonon coupling included via a polaron-transformed tight-binding Hamiltonian (PTTBH) leads to the experimentally observed temperature trends of conductivity. We sample the electron DOS calculated from a modified Arkhipov model that includes doping-induced energetic disorder and carrier screening, and set the resulting energies as diagonal terms of the PTTBH. The hopping integral, t, in the off-diagonal terms decreases with temperature because of an additional electronic coupling term in the PTTBH. We show that the temperature dependence of this coupling term is responsible for the behavior, since the transition matrix elements quadratically depend on T. The coupling term depends on the phonon spectral density, and we show that CPs with a narrower vibrational bandwidth, which is synonymous with softer and/or denser CPs, will exhibit a decrease of with temperature. Our findings complement the fundamental understanding of transport in CPs and provide novel venues to engineer their properties.