Theoretical study on the effects of polarons on the transport properties of anatase TiO₂

We present a theoretical study on the effects of electron-phonon interactions on the transport properties of anatase TiO₂. Temperature-dependent resistivity measurement on anatase TiO₂ thin film has shown that carrier concentrations and temperatures affect the resistivity of this material. At low carrier concentrations, a metal to insulator transition could be observed, while at high carrier concentrations this material only shows metal-like resistivity. In this study we aim to investigate the behaviour of temperature-dependent resistivity at various carrier concentrations as revealed in the experimental study. We hypothesize that electron-phonon interactions with intermediate coupling constant govern the transport properties of this material. We construct Holstein model Hamiltonian incorporating both conduction and valence bands of anatase TiO₂ within parabolic dispersion approximation. We solve the model within the Dynamical Mean Field Theory (DMFT). We calculate the density of states of the system and the corresponding inverse of the square of the density of states at the chemical potential, which is approximately proportional to the resistivity, as a function of temperature. Using carrier concentration values taken as in the experimental data, the calculations show that only insulating phase is found in the low carrier concentrations regime. Meanwhile, at high carrier concentrations, the results show metal-like properties, in agreement with the experimental data.