Theory of the electron phonon relaxation time in cuprates: Reproducing the observed temperature behaviour

TL;DR

This paper models the temperature dependence of electron-phonon energy transfer in cuprates, showing a T^5 dependence at low temperatures and T at high temperatures, aligning with experimental observations.

Contribution

It introduces a theoretical model for electron-phonon relaxation in cuprates considering linear electronic dispersion near nodal points, reproducing observed temperature behaviors.

Findings

Energy transfer rate ∝ T^5 at low T

Energy transfer rate ∝ T at high T

Electron-phonon relaxation time ∝ T^{-3}

Abstract

We have studied the temperature dependence of the rate of energy transfer from electronic sub-system to phononic sub-system in the case of cuprates, when the system is photo-excited by a femtosecond laser pulse. In the pseudogap state, taking the electronic dispersion {\it as linear} near the nodal points of the Brillouin zone, we show that the rate of energy transfer from electronic sub-system to phononic sub-system is proportional to $T^{5}$ at lower temperatures ($T<<T_0$), and is proportional to $T$ at higher temperatures ($T>>T_0$), here $T_0$ is the Debye temperature for cuprates. The linear electronic dispersion in the pseudogap state introduces new terms in the expression of energy transfer as given by M. I. KAGANOV et.al. \cite{kaganov}. {\it But the leading terms are the same which are found in the case of metals in the above reference.} The electron-phonon relaxation time follows $T^{-3}$ law for cuprates which agrees well with the experimental results \cite{demsar,Jdemsar}.