ARPES is a very powerful experimental technique to directly measure electronic properties and self-energy effects such as electronic correlations. ARPES technique is an application of Einstein's photoelectric effect, which measures the energy and angle of electrons ejected from a surface shined by photon sources. Energy and momentum conservations tell us how electrons are bound within the crystal.

More specifically, the photo-electron intensity is given by the product of A(k,w) and M_i,f. A(k,w) is a direct manifestation of electron band structure and electronic correlations, which has contributed ARPES to become one of the powerful tools in study of condensed matters.

M_i,f not only describes photoemission process, but also provides a direct measurement of Berry's phase (one of the beautiful example of quantum physics) and the sign of hopping integrals within the tight-bidning formalism (that has never been determined for any system by any experimental method) of graphene.

Journal of Electron Spectroscopy and Related Phenomena 198, 1 (2015)
Physical Review B 84, 125422 (2011)