Universal scaling of the critical temperature and the strange-metal scattering rate in unconventional superconductors

Abstract Dramatic evolution of properties with minute change in the doping level is a hallmark of the complex chemistry which governs copper oxide superconductivity as manifested in the celebrated superconducting domes as well as quantum criticality taking place at precise compositions. The strange metal state, where the resistivity varies linearly with temperature, has emerged as a central feature in the normal state of copper oxide superconductors. The ubiquity of this behavior signals an intimate link between the scattering mechanism and superconductivity. However, a clear quantitative picture of the correlation has been lacking. Here, we report the observation of quantitative scaling laws between the superconducting transition temperature Tc and the scattering rate associated with the strange metal state in electron-doped copper oxide La2-xCexCuO4 (LCCO) as a precise function of the doping level (x). High-resolution characterization of epitaxial composition-spread films, which encompass the entire overdoped range of LCCO has allowed us to systematically map its structural and transport properties with unprecedented accuracy and increment of Δx = 0.0015. We have uncovered the relations Tc ~ (xc-x)0.5 ~ (A1)0.5, where xc is the critical doping where superconductivity disappears on the overdoped side and A1 is the scattering rate of perfect T-linear resistivity per CuO2 plane. We argue that the striking similarity of the Tc vs A1 relation among copper oxides, iron-based and organic superconductors is an indication of a common mechanism of the strange metal behavior and unconventional superconductivity in these systems.