Scattering effects from neighboring atoms in core-level WSe2 photoemission

Methods of attosecond science originally developed to investigate systems in the gas phase are currently being adapted to obtain temporal information on the electron dynamics that takes place in condensed-matter systems. In particular, streaking measurements have recently been performed to determine photoemission time delays from the ${\mathrm{WSe}}_{2}$ dichalcogenide. In this work we present a fully atomistic description of the photoemission process in ${\mathrm{WSe}}_{2}$ and provide angularly resolved photoemission cross sections and time delays from the W $4f$, Se $3d$ and Se $4s$ core states of the system. Since these states are spatially localized, we propose a cluster approach in which we build up from smaller to larger clusters, so that we can assess the importance of scattering effects by each new layer of neighboring atoms. We use a static-exchange density functional theory method with $B$-spline functions, where a one-center angular-momentum expansion is supplemented by off-center expansions with fewer partial waves. This enhances convergence in comparison with a one-center expansion, which would require very high angular momenta to characterize the localized fast oscillations near each off-center atomic core. We find that the photoemission delays and fully differential cross sections are strongly affected by scattering events that take place off the neighboring atoms, implying the need to consider their effects for quantitative descriptions of the photoemission process.