Universal Planckian dissipation in the strange metal state of the cuprates

A major puzzle in high-T_c superconductivity is the origin of the "Planckian" relaxation rate 1/τ underlying the linear-in-temperature resistivity in the strange-metal state, which persists up to very high temperatures. Implicit in theoretical discussions is the assumption that 1/τ must be universal. Experimentally, it is unclear, however, how such universality can be reconciled with the observed strong doping dependence of the resistivity over a wide doping range. We show, through an analysis of a large body of optical conductivity and electrical resistivity data, that a universal 1/τ requires only that the square optical plasma frequency ${\omega }_{\mathrm{opt}}^2\left(p\right)$ scales linearly with hole doping p across the entire doping range, as is observed experimentally. We further argue that this can be understood via a Gutzwiller factor in doped Mott insulators of the form proposed by Anderson.