Non-equilibrium dynamics of photo-excited electrons in graphene: collinear scattering, Auger processes, and the impact of screening

TL;DR

This paper investigates the ultrafast non-equilibrium behavior of photo-excited electrons in graphene, emphasizing collinear scattering, Auger processes, and the effects of screening, using a combined analytical and numerical approach.

Contribution

It provides an analytical treatment of electron-electron interactions in graphene, highlighting the role of screening and lifetime effects in collinear scattering and Auger processes.

Findings

Carrier multiplication and Auger recombination are significant in graphene.

Screening effects can suppress or enhance scattering processes.

Electron lifetime effects regularize phase space for collinear scattering.

Abstract

We present a combined analytical and numerical study of the early stages (sub-100fs) of the non-equilibrium dynamics of photo-excited electrons in graphene. We employ the semiclassical Boltzmann equation with a collision integral that includes contributions from electron-electron (e-e) and electron-optical phonon interactions. Taking advantage of circular symmetry and employing the massless Dirac Fermion (MDF) Hamiltonian, we are able to perform an essentially analytical study of the e-e contribution to the collision integral. This allows us to take particular care of subtle collinear scattering processes - processes in which incoming and outgoing momenta of the scattering particles lie on the same line - including carrier multiplication (CM) and Auger recombination (AR). These processes have a vanishing phase space for two dimensional MDF bare bands. However, we argue that electron-lifetime effects, seen in experiments based on angle-resolved photoemission spectroscopy, provide a natural pathway to regularize this pathology, yielding a finite contribution due to CM and AR to the Coulomb collision integral. Finally, we discuss in detail the role of physics beyond the Fermi golden rule by including screening in the matrix element of the Coulomb interaction at the level of the Random Phase Approximation (RPA), focusing in particular on the consequences of various approximations including static RPA screening, which maximizes the impact of CM and AR processes, and dynamical RPA screening, which completely suppresses them.