Thermalization and possible signatures of quantum chaos in complex crystalline materials

Significance Quantum chaos has been suggested as a framework to understand transport of charge excitations in strongly correlated electron systems exhibiting the “strange metal” state without long-lived quasiparticle excitations. Identifying a characteristic local scrambling time and a velocity by which perturbation propagates into nonlocal degrees of freedom, a chaos diffusivity is identified and related to the measured charge and energy diffusivities. Here we scrutinize the underlying hypothesis that lattice dynamics can be ignored, particularly at high temperatures, where many phonon bands and their interactions dominate the thermal transport in complex materials. We argue that much of the chaotic behavior, which is also identified in complex insulators, originates from phonons, and in equivalent itinerant systems only the thermal (energy) diffusivity describes chaos diffusivity. Analyses of thermal diffusivity data on complex insulators and on strongly correlated electron systems hosted in similar complex crystal structures suggest that quantum chaos is a good description for thermalization processes in these systems, particularly in the high-temperature regime where the many phonon bands and their interactions dominate the thermal transport. Here we observe that for these systems diffusive thermal transport is controlled by a universal Planckian timescale τ∼ℏ/kBT and a unique velocity vE. Specifically, vE≈vph for complex insulators, and vph≲vE≪vF in the presence of strongly correlated itinerant electrons (vph and vF are the phonon and electron velocities, respectively). For the complex correlated electron systems we further show that charge diffusivity, while also reaching the Planckian relaxation bound, is largely dominated by the Fermi velocity of the electrons, hence suggesting that it is only the thermal (energy) diffusivity that describes chaos diffusivity.