A comparative study of (BI)polaronic (super)conductivity in high- and low- Tc superconducting oxides

A comparative study is made on the conductivity and superconductivity mechanisms in the series of superconducting oxides SrTiO _3-δT _c⋍0.3 K), BaPb _{1- x}Bi _xO ₃(T _c⋍12 K), Li _{1+ x}Ti _{2- x}O ₄(T _c⋍11 K), La _{2- x}Sr _xCuO ₄(T _c⋍40 K), and YBa ₂Cu ₃O _{7-δ (T c⋍60 K for δ⋍0.3-0.4; T c⋍90 K for δ⋍0} ). We claim that all these materials can be viewed as doped semiconductors, where the conductivity is due to doping or self-doping. This procedures mixed-valence conditions for the metal-ions, leading to the formation of small-polarons, namely the combination of the metal atom with its extra charge plus its deformed oxygen coordination. The mobility of the small-polarons is ensured through the mixed-valence charge transfer mechanism. They may be viewed as a dilute gas of charged particles on a lattice, moving in the random fluctuating potential due to the impurities. By varying the concentration of these, small-polarons metal-insulator transitions (probably of the Anderson type) occur in all these materials, which explaines the observed behaviour of the conductivity and points to a universal “minimum conductivity”, σ _min⋍10 ² (Ω cm) ^-1. The special non-linear (solitonic) features of these mixed-valence small-polarons are pointed out. It is further argued that under special conditions these small-polarons, may combine to form small-bipolarons, and the possible binding mechanism for each of the materials is investigated. The superconductivity may then be explained in terms of a Bose-Einstein condensation of these bipolarons, for which the theory has been developed in the last few years. To substantiate our arguments, a short overview of these theoretical results is given. In addition quite a number of relevant experimental data available in the literature on these compounds is reanalysed in terms of the above concepts.