Universal scaling of length, time, and energy for cuprate superconductors based on photoemission measurements of Bi2Sr2CaCu2O8+{δ}

A microscopic scaling relation linking the normal and superconducting states of the cuprates in the presence of a pseudogap is presented using angle-resolved photoemission spectroscopy. This scaling relation, complementary to the bulk universal scaling relation embodied by Homes' law, explicitly connects the momentum-dependent amplitude of the d-wave superconducting order parameter at T\sim0 to quasiparticle scattering mechanisms operative at T\gtrsimTc. The form of the scaling is proposed to be a consequence of the marginal Fermi-liquid phenomenology and the inherently strong dissipation of the normal pseudogap state of the cuprates.