An experimentalist's guide to the matrix element in angle resolved photoemission

•An introduction to the art of angle resolved photoemission is presented.•Matrix element effects are described by a nearly free electron final state model.•ARPES spectral weight of a Bloch band can be calculated from the Fourier transform of its Wannier orbital.•Experimental handedness and improper polarization introduce dichroism.•Instructive showcases from modern ARPES are discussed in detail. Angle resolved photoemission spectroscopy (ARPES) is commonly known as a powerful probe of the one-electron removal spectral function in ordered solid state. With increasing efficiency of light sources and spectrometers, experiments over a wide range of emission angles become more and more common. Consequently, the angular variation of ARPES spectral weight – often times termed “matrix element effect” – enters as an additional source of information. In this tutorial, we develop a simple but instructive free electron final state approach based on the three-step model to describe the intensity distribution in ARPES. We find a compact expression showing that the ARPES spectral weight of a given Bloch band is essentially determined by the momentum distribution (the Fourier transform) of its associated Wannier orbital – times a polarization dependent pre-factor. While the former is giving direct information on the symmetry and shape of the electronic wave function, the latter can give rise to surprising geometric effects. We discuss a variety of modern and instructive experimental showcases for which this simplistic formalism works astonishingly well and discuss the limits of this approach.