Simple extension of the plane-wave final state in photoemission: Bringing understanding to the photon-energy dependence of two-dimensional materials - Christian S. Kern; Anja Haags; Larissa Egger; Xiaosheng Yang; Hans Kirschner; Susanne Wolff; Thomas Seyller; Alexander Gottwald; Mathias Richter; Umberto De Giovannini; Angel Rubio; Michael G. Ramsey; et al. (Physical Review Research, 2023)
Angle-resolved photoemission spectroscopy (ARPES) is a method that measures orbital and band structure contrast through the momentum distribution of photoelectrons. Its simplest interpretation is obtained in the plane-wave approximation, according to which photoelectrons propagate freely to the detector. The photoelectron momentum distribution is then essentially given by the Fourier transform of the real-space orbital. While the plane-wave approximation is remarkably successful in describing the momentum distributions of aromatic compounds, it generally fails to capture kinetic-energy-dependent final-state interference and dichroism effects. Focusing our present study on quasi-freestanding monolayer graphene as the archetypical two-dimensional (2D) material, we observe an exemplary E_{kin}-dependent modulation of, and a redistribution of spectral weight within, its characteristic horseshoe signature around the K[over ¯] and K[over ¯]^{′} points: both effects indeed cannot be rationalized by the plane-wave final state. Our data are, however, in remarkable agreement with ab initio time-dependent density functional simulations of a freestanding graphene layer and can be explained by a simple extension of the plane-wave final state, permitting the two dipole-allowed partial waves emitted from the C 2p_{z} orbitals to scatter in the potential of their immediate surroundings. Exploiting the absolute photon flux calibration of the Metrology Light Source, this scattered-wave approximation allows us to extract E_{kin}-dependent amplitudes and phases of both partial waves directly from photoemission data. The scattered-wave approximation thus represents a powerful yet intuitive refinement of the plane-wave final state in photoemission of 2D materials and beyond.