Correlation between the strength of low-temperature T-linear normal-state resistivity and $T_{\rm c}$ in overdoped electron-doped cuprate superconductors

Abstract: The recently observed an intimate link between the nature of the strange metallic normal-state and superconductivity in the overdoped electron-doped cuprate superconductors is calling for an explanation. Here the intrinsic correlation between the strength of the low-temperature linear-in-temperature normal-state resistivity and superconducting transition temperature $T_{\rm c}$ in the overdoped electron-doped cuprate superconductors is studied within the framework of the kinetic-energy-driven superconductivity. On the one hand, the main ingredient is identified into a electron pairing mechanism involving the spin excitation, and then $T_{\rm c}$ has a dome-like shape doping dependence with the maximal $T_{\rm c}$ that occurs at around the optimal electron doping. On the other hand, in the normal-state above $T_{\rm c}$, the low-temperature linear-in-temperature normal-state resistivity in the overdoped regime arises from the momentum relaxation due to the electron umklapp scattering mediated by the same spin excitation. This same spin excitation that governs both the electron umklapp scattering responsible for the low-temperature linear-in-temperature normal-state resistivity and electron pairing responsible for superconductivity naturally generates a correlation between the strength of the low-temperature linear-in-temperature normal-state resistivity and $T_{\rm c}$ in the overdoped regime.