Universal $T$-linear resistivity and Planckian limit in overdoped cuprates

The perfectly linear temperature dependence of the electrical resistivity observed as T → 0 in a variety of metals close to a quantum critical point1–4 is a major puzzle of condensed-matter physics5. Here we show that T-linear resistivity as T → 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bilayer cuprate Bi2Sr2CaCu2O8+δ and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi2Sr2CuO6+δ (ref. 6), La1.6−xNd0.4SrxCuO4 (ref. 7) and La2−xSrxCuO4 (ref. 8), despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the T-linear coefficient (per CuO2 plane), A1□, is given by the universal relation A1□TF = h/2e2, where e is the electron charge, h is the Planck constant and TF is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1/τ of charge carriers reaches the Planckian limit9,10, whereby ħ/τ = kBT, works not only for hole-doped cuprates6–8,11,12 but also for electron-doped cuprates13,14, despite the different nature of their quantum critical point and strength of their electron correlations.