Power Law Liquid -- A Unified Form of Low-Energy Nodal Electronic Interactions in Hole Doped Cuprate Superconductors

Based upon detailed ARPES measurements of Bi2Sr2CaCu2O8$+\delta $ over a wide range of doping levels, we present a new unifying phenomenology for the non-Fermi liquid normal-state interactions (scattering rates) in the nodal direction. This new phenomenology has a continuously varying power law exponent (hence named a Power Law Liquid or PLL), which with doping varies smoothly from a quadratic Fermi Liquid to a linear Marginal Fermi Liquid and beyond. Using the extracted PLL parameters we can calculate the optics and resistivity over a wide range of doping and normal-state temperature values, with the results closely matching the experimental curves. This agreement includes the presence of the T* ``pseudogap'' temperature scale observed in the resistivity curves including the apparent quantum critical point.