Energy Relaxation and Dynamics in the Correlated Metal Sr2RuO4 via Terahertz Two-Dimensional Coherent Spectroscopy

Discriminating the effects of different kinds of scattering in strongly interacting metals is crucial in their understanding. While momentum or current relaxation can be readily probed via dc resistivity or linear terahertz (THz) spectroscopy, discriminating other kinds of scattering can be more challenging. In this Letter, we argue that the nonlinear optical technique of THz 2D coherent spectroscopy measures the energy relaxation rate in strongly interacting metals. We apply the technique to the Fermi liquid Sr_{2}RuO_{4} and observe two energy relaxation channels: a fast process (∼0.1 THz) that we interpret as energy loss to the phonon system and a much slower relaxation (≲1 GHz) that we interpret as the relaxation of nonequilibrium phonons. Both rates are at least an order of magnitude slower than the momentum relaxation rate. We show how energy relaxation provides a unique diagnostic into certain kinds of scattering and among other aspects allows a measure of the dimensionless electron-phonon coupling constant. Our observations reveal the versatility of nonlinear THz spectroscopy to measure the energy relaxation dynamics in correlated metals and also highlights the need for improved theoretical understanding of such processes in interacting metals.