ACKNOWLEDGEMENTS SUPPORTING MATERIAL: EXPERIMENTAL AND CALCULATIONAL METH- ODS emission angle might be mistaken for signs of a surface core level shift in graphite because of the higher surface sensitivity for off-normal emission. Ignoring dispersion effects might play some role in the recent dispute about the existence of a surface core level shift in graphite [7–10], but note that the interference effect reported here is inconsistent with the observation of multiple C 1 s components. Here we can state that to a good approximation either the bonding or the anti-bonding band can be observed in any given emission direction. In conclusion, we have shown that the interaction between the two atoms in the unit cell of graphene is sufficiently strong to induce the formation of a σ -band derived from the carbon 1 s state. Interference effects in the photoemission process give rise to a strong suppression of either the bonding or the anti-bonding band for different emission directions, such that the absolute size of the splitting could be determined from the entire data set. The interference effect furthermore allows to observe only the bonding or the anti-bonding states under certain conditions, opening the unique opportunity for detailed and possibly local as well as time-resolved studies of bonding in solids. We gratefully acknowledge stimulating discussions with Gustav Bihlmayer, D. L. Mills and Javier Garc´ıa de Abajo. The research leading to these results has received funding from the Danish National Research Council, the Lundbeck Foundation and the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 226716. GZ thanks ANPCyT of Argentina and the ICTP Trieste for financial support under the TRIL Programme. The graphene film on Ir(111) was prepared in situ using standard procedures [11] and the sample quality and cleanliness was monitored by low energy electron diffraction (LEED) and x-ray photoelectron spectroscopy. Angle-resolved photoemission data were taken at the SuperESCA beamline of the storage ring ELETTRA. The experimental chamber is equipped with a 150 mm electron energy analyser from SPECS, implemented with a delay line detector 9