Scaling of the strange-metal scattering in unconventional superconductors.

Marked evolution of properties with minute changes in the doping level is a hallmark of the complex chemistry that governs copper oxide superconductivity as manifested in the celebrated superconducting domes and quantum criticality taking place at precise compositions 1-4 . The strange-metal state, in which the resistivity varies linearly with temperature, has emerged as a central feature in the normal state of copper oxide superconductors 5-9 . The ubiquity of this behaviour signals an intimate link between the scattering mechanism and superconductivity 10-12 . However, a clear quantitative picture of the correlation has been lacking. Here we report the observation of precise quantitative scaling laws among the superconducting transition temperature (T c ), the linear-in-T scattering coefficient (A 1 ) and the doping level (x) in electron-doped copper oxide La 2-x Ce x CuO 4 (LCCO). High-resolution characterization of epitaxial composition-spread films, which encompass the entire overdoped range of LCCO, has enabled us to systematically map its structural and transport properties with unprecedented accuracy and with increments of Δx = 0.0015. We have uncovered the relations T c ~ (x c - x) 0.5 ~ (A 1 □ ) 0.5 , where x c is the critical doping in which superconductivity disappears and A 1 □ is the coefficient of the linear resistivity per CuO 2 plane. The striking similarity of the T c versus A 1 □ relation among copper oxides, iron-based and organic superconductors may be an indication of a common mechanism of the strange-metal behaviour and unconventional superconductivity in these systems.