Figure 3: Unoccupied bands for monolayer, bilayer and trilayer graphene.

(a) The IV-minima, shown as white circles in Fig. 2a–c, are plotted together with the calculated band, formed from interlayer states, for graphite (adapted from ref. 24). Red circles, blue triangles and black squares correspond to the data from the monolayer, bilayer and trilayer pixel indicated in Fig. 1a. The difference between the two energy axes with respect to the vacuum and Fermi level is given by the work functions of graphite³² Φ=4.6 eV. The observed behaviour can be understood in a tight-binding-like picture where the interlayer states resemble atomic orbitals. (b) Schematic that shows how an ‘atomic’ monolayer state (red) splits into a ‘binding’ and an ‘anti-binding’ state (blue) and then in three trimer-states (black). The splitting energies of 2t and are defined by the interaction strength t between different interlayer states. The continuous graphite band (grey area) of width 4t envelopes the quantized monolayer, bilayer and trilayer states. This is expected from the tight-binding picture, as graphite represents an infinite chain of interlayer states.