Random resistivity network calculations for cuprate superconductors with an electronic phase separation transition

The resistivity as a function of temperature for high temperature superconductors is very unusual and, despite its importance, lacks a unified theoretical explanation. It is linear with the temperature for overdoped compounds but it falls more quickly as the doping level decreases. The resistivity of underdoped cuprates increases like that of an insulator below a characteristic temperature where it shows a minimum. We show that this overall behavior can be explained by calculations using an electronic phase segregation into two main component phases with low and high electronic densities. The total resistance is calculated from the various contributions through several processes of random picking of the local resistivities and using a common statistical random resistor network approach.