Linear-in temperature resistivity from an isotropic Planckian scattering rate

A variety of ‘strange metals’ exhibit resistivity that decreases linearly with temperature as the temperature decreases to zero 1 – 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 ħ / τ = αk B T , where α is a constant of order unity, ħ is the Planck constant and k B 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 scattering—the ‘Planckian limit’ 4 , 5 —but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance of La 1.6− x Nd 0.4 Sr x CuO 4 —a hole-doped cuprate that shows linear-in-temperature resistivity down to the lowest measured temperatures 6 . The angle-dependent magnetoresistance shows a well defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy measurements 7 and reveals a linear-in-temperature scattering rate that saturates at the Planckian limit, namely α = 1.2 ± 0.4. Remarkably, we find that this Planckian scattering rate is isotropic, that is, it is independent of direction, in contrast to expectations from ‘hotspot’ models 8 , 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.