Energy Relaxation and dynamics in the correlated metal Sr$_2$RuO$_4$ via THz two-dimensional coherent spectroscopy

TL;DR

This study uses nonlinear THz 2D spectroscopy to measure energy relaxation channels in the correlated metal Sr$_2$RuO$_4$, revealing distinct inelastic scattering processes and their timescales, advancing understanding of electron-bath interactions.

Contribution

First application of nonlinear THz 2D spectroscopy to distinguish energy relaxation channels in a strongly correlated metal, providing new insights into inelastic scattering mechanisms.

Findings

Identified two energy relaxation channels: fast phonon energy loss and slow phonon thermalization.

Fast energy relaxation is significantly slower than momentum relaxation, indicating strong electron interactions.

Slow relaxation occurs on sub-GHz timescale, consistent with non-equilibrium phonon dynamics.

Abstract

Separating out the contributions of different scattering channels in strongly interacting metals is crucial in identifying the mechanisms that govern their properties. While momentum or current relaxation rates can be readily probed via \textit{dc} resistivity or optical/THz spectroscopy, distinguishing different kinds of inelastic scattering can be more challenging. Using nonlinear THz 2D coherent spectroscopy, we measure the rates of energy relaxation after THz excitation in the strongly interacting Fermi liquid, Sr$_2$RuO$_4$. Energy relaxation is a bound on the total scattering and specifically a measure of contributions to the electron self-energy that arise from {\it inelastic} coupling to a bath. We observe two distinct energy relaxation channels: a fast process that we interpret as energy loss to the phonon system and a much slower relaxation that we interpret as arising from a non-equilibrium phonon effects and subsequent heat loss through diffusion. Interestingly, even the faster energy relaxation rate is at least an order of magnitude slower than the overall momentum relaxation rate, consistent with strong electron interactions and the dominance of energy-conserving umklapp or interband electron-electron scattering in momentum relaxation. The slowest energy relaxation rate decays on a sub-GHz scale, consistent with the relaxation dynamics of non-equilibrium phonons. Our observations reveal the versatility of nonlinear THz spectroscopy to measure the energy relaxation dynamics in correlated metals. Our work also highlights the need for improved theoretical understanding of such processes in interacting metals.