11 [1] Kempgens, B., K¨ oppel, H., Kivim¨ aki, A., Neeb, M., Cederbaum, L. S., and Bradshaw, A. M. Physical Review Letters 79 , 3617 (1997). [2] Hergenhahn, U., Kugeler, O., Rudel, A., Rennie, E. E., and Bradshaw, A. M. Journal of Physical Chemistry A 105 (23), 5704–5708 (2001). [3] Takata, Y., Kayanuma, Y., Yabashi, M., Tamasaku, K., Nishino, Y., Miwa, D., Harada, Y., as the incoherent sum of the intensities for the two atoms in the graphene unit cell. This approach might, at first sight, appear inconsistent with the main conclusion of this paper that the 1 s state is described as an extended coherent wave function. Note, however, that what we calculate and compare to is the sum of the bonding and anti-bonding states. The sum of the probability density for the wave functions is strongly peaked at the atomic cores, independent of the wave vector chosen. Consequently, one would expect the same photoe- mission signal, including final-state diffraction effects, as from the sum of all core states. The simulations were performed on a flat, free-standing graphene layer. The lattice param- eter was set to 2.466 ˚ A. The influence of the underlying Ir(111) substrate, that of small changes of the lattice parameter, as well as that of a relatively small corrugation of the graphene layer with moir´ e periodicity [14] was tested. No significant changes were found in the diffraction patterns. Parameters for the calculations are: V$_{0}$ = 8 eV, linear polarization, angle between incoming light and analyzer 70 $^{◦}$, angular acceptance 10$^{◦}$, system at room temperature. The Debye temperature of graphene is much higher than this and hence its precise value does not lead to any noticeable differences in the result. As seen in Fig. 2 the agreement between these calculation and the data is excellent with the two being nearly indistinguishable. However, in order to obtain this agreement, the photoelectron’s kinetic energy in the simulation had to be assumed to be 12 eV lower than that in the experiment. The reason for this is presently unknown. The tight-binding calculations for the band structure and photoemission intensity in Fig. 3 are very similar to those presented for the π -valence band in Ref. [5], but use σ -band symmetry instead. The parameters used for the calculation are inspired by the experimental binding energy and band width but they are only chosen for illustrative purposes. Their precise value is irrelevant for the conclusions of this paper.