Universal Planckian relaxation in the strange metal state of the cuprates

TL;DR

This paper provides evidence that the Planckian relaxation rate in the strange metal state of cuprates is doping-independent, suggesting a universal relaxation mechanism, while the doping dependence of resistivity slope is due to effective mass enhancement.

Contribution

The study demonstrates that the Planckian relaxation rate remains universal across doping levels, challenging previous assumptions of doping dependence, and links the doping dependence of resistivity to effective mass enhancement.

Findings

The plasma frequency squared scales linearly with doping p.

The relaxation rate 1/τ is doping-independent across the strange metal state.

Doping dependence of resistivity slope arises from effective mass enhancement.

Abstract

A major puzzle in understanding high-$T_{\rm c}$ superconductivity is the microscopic origin of the linear-in-temperature ($T$-linear) resistivity in the strange metal state, which persists up to very high temperatures. Implicit to existing theoretical discussions of this universal `{Planckian}' relaxation rate is the assumption that it must also be independent of doping, $p$. Applied to the cuprates, however, this apparently contradicts the observed strong doping-dependence ($\propto 1/p$) of the slope of the $T$-linear resistivity over a wide doping range. Here, we show through a combination of measurements, including optical conductivity and entropy, that the plasma frequency squared $\omega_p^2$ scales as $p$ over a similar doping range. Together, these dependences provide compelling evidence that the relaxation rate $1/\tau$ is indeed doping-independent (i.e. universal) throughout the entire strange metal state. Furthermore, we argue that the entire doping dependence of $\omega_p^2$ can be understood to arise from an effective mass enhancement of a specific form proposed by Anderson [\emph{Science} \textbf{235}, 1196 (1987)] in the context of doped Mott insulators. Such a mass enhancement originates from strong short-range repulsive interactions, while the Planckian relaxation rate itself appears to be an emergent phenomenon of independent physical origin.