Electron-Phonon Relaxation Time in Cuprates: Reproducing the Observed Temperature Behavior YPM 2015 Rukmani Bai 11 th March, 2015

Outline  Objective  Pump-Probe Spectroscopy  Two Temperature Model  Relaxation Time in metals  Relaxation Time in Cuprates  Conclusion

Objective In simple metals electron dynamics is well understood. The Kaganov-Lifshitz-Tanatarov (KLT) model is well established. But in the case of strongly correlated systems like Cuprate superconductors in their normal state, there exists no theoretical model to describe electron relaxation. In these systems one of the complications is the strong electron- electron correlation and very different electronic dispersion from metals.

Pump Probe Spectroscopy Ref.

Two Temperature Model N. SINGH, Int. J. Mod. Phys. B, 24, 1141 (2010)

contd... M. L. Schneider et al. Europhys. Lett., 60 (3), pp. 460–466 (2002)

Relaxation Time in Metals Electrons and Phonons follow FD and BE distributions respectively. When pump pulse excites the electrons and these electrons form Non Fermi Dirac (NFD) distribution. As Te >> T, electrons transfer their energy to phonons to relax the system. Energy transfer and relaxation time depend on temperature.

Relaxation Time in Metals ( KLT Model ) Energy transferred by electrons to phonons per unit time per unit volume is Here change in number of phonons per unit volume per unit time is 1414 This is Bloch-Boltzmann-Peierls equation. Here k = k' – f

contd..... Thus energy transfer from electrons to phonons per unit time per unit volume

Relaxation Time From heat balance equation: Solution of this equation is: Where k is an integral constant and τ ep is electron-phonon relaxation time B Where

Relaxation Time Thus electron-phonon relaxation time for metals becomes:

Follow linear dispersion relation at the node which is different from metals. As pump pulse passes through sample it excites nodal QPs because energy gap is zero in this region as compare to anti- nodal region. There is an extra term in the energy relation due to this linear dispersion. Cuprates

Relaxation Time in Cuprates A modification of KLT model: Energy transferred by electrons to phonons per unit time per unit volume is Here change in number of phonons per unit volume per unit time is 1414 This is Bloch-Boltzmann-Peierls equation. Here k = k' – f

Cuprates (Low Temperature) Energy transfer from electrons to phonons for cuprates Dispersion relation 8 8

Cuprates (High Temperature)

Relaxation Time for Cuprates The electron-phonon relaxation time in cuprates in low temperature comes out to be: t The calculated relaxation time turns out to have the same Temperature dependence as in metals

Comparison (Result) R. Bai, P. Bhalla, N. Singh : arXiv:

Conclusions Energy transfer rate in metals varies with temperature as T 5 and T for low and high temperature. Due to linear dispersion relation at the nodal point it is having two terms in cuprates. Relaxation time in metals and cuprates varies with temperature as T -3 for low temperature region. We have reproduced the experimentally discovered T -3 law for relaxation time for cuprates. Thank You