Universal sheet resistance of the cuprate superconductors

Upon introducing charge carriers into the underlying copper-oxygen sheets of the cuprates, the parent insulator evolves into a superconductor and eventually into a seemingly conventional Fermi liquid. Much has remained elusive about the nature of this evolution, and about the peculiar metallic state at intermediate hole-carrier concentrations ($p)$, where the planar resistivity exhibits a linear temperature dependence ($\rho \propto T)$ that is disrupted upon cooling toward the superconducting state by the opening of a `pseudogap' along the Fermi surface. Here we demonstrate for the quintessential compound HgBa$_{\mathrm{2}}$CuO$_{\mathrm{4+\delta }}$ a purely Fermi-liquid-like resistivity ($\rho \propto T^{\mathrm{2}})$ deep in the pseudogap regime. Our result when combined with select prior work for other compounds reveals the fundamental resistance per copper-oxygen sheet in both the linear ($\rho_{\mathrm{S}}=A_{\mathrm{1S}}T)$ and quadratic ($\rho_{\mathrm{S}}=A_{\mathrm{2S}}T^{\mathrm{2}})$ regimes, with $A_{\mathrm{1S\thinspace }}\propto \quad A_{\mathrm{2S\thinspace }}\propto $ 1/$p$. Theoretical models for the cuprates can now be benchmarked against this remarkably simple universal behavior. \textit{Preprint: arXiv:1207.1504. }Work supported by DOE-BES.