New models for the positive and negative temperature coefficients of resistivity for TiO0.80−1.23metallic oxides

A reexamination is made of previous resistivity data of the Ti${\mathrm{O}}_{0.80-1.23}$ metallic oxide system, in which very large positive and negative temperature coefficients of resistivity $\alpha$ are observed. Ti${\mathrm{O}}_{0.80-1.23}$ samples contain a large number of stoichiometric vacancies which can be thermally ordered and disordered, drastically changing the residual resistivity, without seriously affecting the superconducting $T_c$. Fitting the results to the two-level model shows that any resistivity due to the two-level system must operate in parallel with the normal electron-phonon interactions. A phenomenological formula, based on the ideas of incipient localization in very-high-resistivity materials, is introduced. This formula fits all the data for the Ti${\mathrm{O}}_{0.80-1.23}$ system in a semiquantitative way. It also predicts that a zero $\alpha$ (the Mooij criterion) occurs when the elastic mean free path and the weak localization coherence length are approximately equal.