Resistivity and superconductivity from anharmonic phonons

The electrical resistivity is calculated for electron scattering from anharmonic phonons. We consider phonon potential energies of the form ∼Qn, as well as double-well potentials ∼Q4-αQ2. For phonon potential energies with a power law ∼Qn, the resistivity at high temperature is proportional to T2/n. At low temperature, the resistivity rises rapidly and then flattens, thereby forming a knee shape. This behavior explains the resistivity of cuprate superconductors in the normal state. We also correlate resistivity with the superconducting transition temperature Tc, to see whether anharmonic phonons cause the pair binding in the superconductor. Our results show that a reasonable set of parameters to explain the resistivity is unable to explain the Tc of these materials.