Nonequilibrium dynamics of photoexcited electrons in graphene: Collinear scattering, Auger processes, and the impact of screening

We present a combined analytical and numerical study of the early stages (sub-100-fs) of the nonequilibrium dynamics of photoexcited 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. © 2013 American Physical Society.

Enduring Borderlands: the Marches of Ireland and Wales in the Early Modern Period

This joint chapter explores similarities and differences between two borderlands within the early modern ‘British’ state – the marches of Ireland and Wales. In some respects, the two regions were very different, most fundamentally because the Irish march remained militarised throughout the Tudor period, while Welsh society was markedly more peaceful. However, there was also much in common. In the later middle ages both marches were frontiers between the expanding Anglo-Normans and native Celtic society. The notion that the march separated ‘civility’ from ‘savagery’ was an enduring one: despite the efforts of the Tudors to impose centralisation and uniformity throughout its territories, there remained institutions, structures of power, and mentalities which ensured that both sets of marches were still in existence by the end of the 16th century. This chapter explores the reasons for the endurance of these borderlands, and indicates how political reforms of the 16th century caused the perception – and sometimes the very location – of the marches to alter.