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Three-dimensional (3D) electronic band structure is fundamental forunderstanding a vast diversity of physical phenomena in solid-state systems,including topological phases, interlayer interactions in van der Waalsmaterials, dimensionality-driven phase transitions, etc. Interpretation ofARPES data in terms of 3D electron dispersions is commonly based on thefree-electron approximation for the photoemission final states. Our soft-X-rayARPES data on Ag metal reveals, however, that even at high excitation energiesthe final states can be a way more complex, incorporating several Bloch waveswith different out-of-plane momenta. Such multiband final states manifestthemselves as a complex structure and excessive broadening of the spectralpeaks from 3D electron states. We analyse the origins of this phenomenon, andtrace it to other materials such as Si and GaN. Our findings are essential foraccurate determination of the 3D band structure over a wide range of materialsand excitation energies in the ARPES experiment.

Are high-energy photoemission final states free-electron-like?