Universal Planckian relaxation in the strange metal state of the cuprates

Abstract

A major puzzle in high-$T_{\rm c}$ 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 $ω_{\rm opt}^2(p)$ scales linearly with $p$ 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 [\emph{Science} \textbf{235}, 1196 (1987)].