The phonon contribution to the low-temperature thermal conductivity in overdoped cuprates: a probe of electron-phonon coupling

In the cuprates, past investigations of the low-temperature ($T < 1$K) thermal conductivity ($\kappa$) have focused on the electronic contribution to $\kappa$. Here we examine the phonon contribution to the thermal conductivity in two families of overdoped cuprates: Tl-2201 and Bi-2201. We find $\kappa_{ph}$ to be proportional to $T^2$ with a magnitude that is independent of sample size (not determined by boundary scattering of the phonons). In Tl2201, $\kappa_{ph}$ is shown to grow with increasing doping. We argue that this term in $\kappa_{ph}$ arises from phonon-electron scattering, providing a measure of electron-phonon coupling in the cuprates. The increase in $\kappa_{ph}$ with increasing doping is indicative of a decrease in the electron-phonon coupling with increasing doping.