Nonequilibrium electron-phonon dynamics with high momentum resolution: Thermalization bottlenecks and the effects of phonon dispersion

Abstract

The nonequilibrium electron-phonon interplay is central to thermalization of solids, yet the microscopic picture of transient states and relaxation pathways remains incomplete. Previous nonequilibrium Green's function (NEGF) studies were restricted to local phonons and local self-energy approximations, leaving momentum-dependent dynamics largely unexplored. In this work, we demonstrate the power of the recently developed quantics-tensor-train (QTT) NEGF framework through large-scale lattice simulations with arbitrary phonon dispersions. QTTs provide a memory-efficient representation of two-time Green's functions, enabling momentum-resolved simulations with full electron-phonon feedback on lattices up to 256x256 sites. Comparing optical and acoustic phonon models, we reveal a hierarchy of relaxation bottlenecks that extends the well-known phonon-window bottleneck effect. For optical phonons, we confirm the main phonon-energy window and uncover a reduced window separating momentum-space regions of excess and deficit electronic population. We also identify a separate bottleneck in phonon thermalization, rooted in the momentum-dependent coupling to the particle-hole continuum. For acoustic phonons, the phonon-energy window acquires pronounced momentum dependence dictated by simultaneous energy-momentum conservation. The reduced window becomes asymmetric; directional scattering between Brillouin-zone regions creates a persistent bottleneck for low-momentum phonon modes. The high momentum and frequency resolution of our spectra further reveals a direct correspondence between phonon relaxation and charge response. Our results establish QTT-NEGF simulations as a scalable and controlled framework for quantitative nonequilibrium electron-phonon dynamics, overcoming previous lattice-size and propagation-time limitations and providing accurate reference data for time-resolved spectroscopies.