excludes the existence of unresolved components, because their intensities would modulate differently, changing the shape of the peak. The left panel of the figure shows the resulting intensity modulation function while the right panel gives the binding energy modulation. The modulation function is compared to the simulation for a flat, free-standing layer of graphene. The agreement between experiment and calculation is excellent. 

The binding energy modulation, on the other hand, is shown as a function of k$_{‖}$ , the wave-vector component parallel to the surface, which is the only relevant wave-vector for a two-dimensional system like graphene. As the portion of the reciprocal space covered by the experiment increases at higher photon energies, a periodic pattern emerges which, however, does not coincide with the reciprocal lattice mesh. At the origin ( k$_{‖}$ = (0 , 0)) the binding energy is always close to its maximum value. The experiments at hν = 400 eV and 500 eV show that the binding energy takes its maximum value also at the next-nearest neighbor reciprocal lattice points, while the experiments at 600 and 700 eV show that this occurs again at the next-nearest neighbors of these latter points. Interestingly, at all the other reciprocal lattice points the binding energy takes its minimum value. The periodic pattern, therefore, is described with two complementary sublattices: the binding energy is at its maximum value at all the points connected by vectors that are √$_{3 times longer than}$ the primitive vectors and rotated by 30 $^{◦}$, and it is at its minimum value at all the other reciprocal lattice points. 

There are, in principle, several different mechanisms which could lead to the observed binding energy variations. The first is the existence of several unresolved components which change their relative intensity due to a final state effect (photoelectron diffraction) and thereby mimic a peak-shift. This appears highly unlikely in the present case, not only be- cause of the excellent agreement with the intensity calculation for a single component, but also because a peak shift of the observed magnitude would essentially require a complete supression of peak intensities in certain directions, and this is unrealistic for a usual pho- toelectron diffraction-type modulation. It would also be very unlikely that the mechanism leads to a binding energy modulation which is periodic in reciprocal space , as seen in Fig. 2. 

The second possible explanation is a recoil effect in which some of the photoelectron’s energy is used to excite lattice vibrations. This effect has been reported for photoemission from the graphite C 1 s state [3]. For increasing photon energies it leads to a decreasing apparent binding energy since some of the photoelectron’s energy remains with the emitting 

