Small-polaron coherent conduction in lightly doped ReTiO$_{3+ \delta/2}$   (Re=La or Nd) thin films prepared by Pulsed Laser Deposition
  LaTiO$_{3+\delta/2}$, NdTiO$_{3+\delta/2}$, and Nd$_{1-x}$Sr$_{x}$TiO$_{3+\delta/2}$ thin films have been epitaxially grown on (100)SrTiO$_{3}$ and (100)LaAlO$_{3}$ single crystal substrates by using the pulsed laser deposition technique. The oxygen pressure during deposition has been carefully controlled to ensure that the films are lightly doped in the metal side near the metal-Mott-insulator boundary. A steep drop of the effective carrier number at low temperatures has been observed in some of the films, which may correspond to a gradually opening of the Spin Density Wave (SDW) gap due to the antiferromagnetic spin fluctuations. At elevated temperatures, a thermally induced decrease of the Hall coefficient can also be clearly observed. In spite of the fact that these films were prepared from different materials in varied deposition conditions, the temperature dependence of their resistance can all be almost perfectly fitted by a small-polaron coherent conduction model ($R_s(T)=R_s(0)+C\omega_\alpha/\sinh^2(T_\omega/T)$). Careful investigation on the fitting parameters implies that the frequency of the phonon coupled to the electrons may be partially related to the lattice distortion induced by the mismatch strain of the substrates. 
J. Li, F.B. Wang, P. Wang, M.J. Zhang, H.Y. Tian, D. N. Zheng