Scaling of the strange-metal scattering in unconventional superconductors

Abstract

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 (A₁) and the doping level (x) in electron-doped copper oxide La_2-xCe_xCuO₄ (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 ~ (A₁^□)^0.5, where x_c is the critical doping in which superconductivity disappears and A₁^□ is the coefficient of the linear resistivity per CuO₂ plane. The striking similarity of the T_c versus A₁^□ 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.