Linear-in temperature resistivity from an isotropic Planckian scattering rate
A variety of â€˜strange metalsâ€™ exhibit resistivity that decreases linearly with temperature as the temperature decreases to zero1â€“3, in contrast to conventional metals where resistivity decreases quadratically with temperature. This linear-in-temperature resistivity has been attributed to charge carriers scattering at a rate given by Ä§/Ï„ = Î±kBT, where Î± is a constant of order unity, Ä§ is the Planck constant and kB is the Boltzmann constant. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scatteringâ€”the â€˜Planckian limitâ€™4,5â€”but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance of La1.6âˆ’xNd0.4SrxCuO4â€”a hole-doped cuprate that shows linear-in-temperature resistivity down to the lowest measured temperatures6. The angle-dependent magnetoresistance shows a well defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy measurements7 and reveals a linear-in-temperature scattering rate that saturates at the Planckian limit, namely Î± = 1.2 Â± 0.4. Remarkably, we find that this Planckian scattering rate is isotropic, that is, it is independent of direction, in contrast to expectations from â€˜hotspotâ€™ models8,9. Our findings suggest that linear-in-temperature resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit. Â© 2021, The Author(s), under exclusive licence to Springer Nature Limited.