Universal $T$-linear resistivity and Planckian dissipation in overdoped cuprates
Résumé
The perfectly linear temperature dependence of the electrical resistivity observed as T$\rightarrow$ 0 in a variety of metals close to a quantum critical point is a major puzzle of condensed-matter physics . Here we show that T-linear resistivity as T$\rightarrow$0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bilayer cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+\lambda}$ and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi$_2$Sr$_2$CuO$_{6+\delta}$ , La$_{1.6−x}$Nd$_{0.4}$Sr$_x$CuO$_4$ and La$_{2−x}$Sr$_x$CuO$_4$ , despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the T-linear coefficient (per CuO$_2$ plane), A1$^□$, is given by the universal relation A1$^□$T$_F$=$h/2e^2$ , where $e$ is the electron charge, $h$ is the Planck constant and $T_F$ is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1/$\tau$ of charge carriers reaches the Planckian limit, whereby $\hbar$/$\tau$=$k_BT$, works not only for holedoped cuprates but also for electron-doped cuprates, despite the different nature of their quantum critical point and strength of their electron correlations.