On the T-linear resistivity of cuprates: theory

TL;DR

This paper develops a theoretical model explaining the T-linear resistivity in optimally doped cuprates by linking electron-paramagnon interactions to quantum critical magnetic fluctuations, emphasizing the role of magnetic correlation length scaling.

Contribution

It introduces a reverse engineering approach to determine the electron-paramagnon coupling that results in T-linear resistivity, highlighting the importance of quantum criticality in cuprates.

Findings

The coupling matrix element scales as 1/(q^2 + ξ(T)^-2).

Magnetic correlation length ξ(T) scales as 1/T in the quantum critical regime.

T-linear resistivity is explained by the temperature dependence of magnetic fluctuations.

Abstract

By partitioning the electronic system of the optimally doped cuprates in two electronic components: (1) mobile electrons on oxygen sub-lattice; and (2) localized spins on copper sub-lattice, and considering the scattering of mobile electrons (on oxygen sub-lattice) via generation of paramagnons in the localized sub-system (copper spins), we ask what should be the electron-paramagnon coupling matrix element $M_q$ so that T-linear resistivity results. This 'reverse engineering approach' leads to $|M_q|^2 \sim \frac{1}{q^2+\xi(T)^{-2}}$. We comment how can such exotic coupling emerge in 2D systems where short range magnetic fluctuations resides. In other words, the role of quantum criticality is found to be crucial. And the T-linear behaviour of resistivity demands that the magnetic correlation length scales as $\xi(T)\propto\frac{1}{T}$, which seems to be a reasonable assumption in the quantum critical regime of cuprates (that is, near optimal doping where T-linear resistivity is observed).