Linear-in temperature resistivity from an isotropic Planckian scattering rate

Abstract

A variety of "strange metals" exhibit resistivity that decreases linearly with temperature as $T\rightarrow 0$, in contrast with conventional metals where resistivity decreases as $T^2$. This $T$-linear resistivity has been attributed to charge carriers scattering at a rate given by $\hbar/\tau=\alpha k_{\rm B} T$, where $\alpha$ is a constant of order unity. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering---the "Planckian limit"---but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance (ADMR) of Nd-LSCO---a hole-doped cuprate that displays $T$-linear resistivity down to the lowest measured temperatures. The ADMR unveils a well-defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy (ARPES) measurements and reveals a $T$-linear scattering rate that saturates the Planckian limit, namely $\alpha = 1.2 \pm 0.4$. Remarkably, we find that this Planckian scattering rate is isotropic, i.e. it is independent of direction, in contrast with expectations from "hot-spot" models. Our findings suggest that $T$-linear resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.