Universal T-linear resistivity and Planckian dissipation in cuprates

The perfectly linear temperature dependence of the electrical resistivity observed as T→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→0 is a generic property of cuprates, associated with a universal scattering rate [1]. We measured the low-temperature resistivity of the bi-layer cuprate Bi2212 and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi2201, Nd-LSCO and LSCO, despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the T-linear coefficient (per CuO₂ plane), A, is given by the universal relation A T_F = h / 2e², 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 /τ of charge carriers reaches the Planckian limit [2], whereby h /τ = 2π k_BT, works not only for hole-doped cuprates but also for electron-doped cuprates, despite the different nature of their quantum critical point and strength of their electron correlations.

[1] Legros et al., Nature Physics (in press); arXiv:1805.02512 (2018).
[2] Bruin et al., Science 339, 804 (2013).