Resistivity saturation in simple models for metals

We study here the electrical resistivity of two simplified models of metals at high temperatures. The ‘metal’ is modelled as a one-dimensional Kronig-Penney chain of potential barriers (the ‘ions’), with the electrons moving independently of each other in the chain. The effect of disorder on the electrons is described in terms of their scattering, either from displaced potential barriers, or from strength-varying barriers. The temperature is introduced via the probability distributions of either the displacements or the strengths of the barriers. At low temperatures both mechanisms of scattering yield the standard result that the resistivity increases linearly with the temperature T. At high temperatures, a saturation of resistivity occurs when the positions are modulated, while in the sfmigf/i-modulation case no saturation results, though the dependence on temperature becomes ‘milder’, i.e. proportional to the square root of T.