The first observation is the variation of conductance of graphite ribbons on the surface of HOPG. The top layer always exhibits more conductance than the lower layers. During the peeling off process the top few layers of graphite peels off inhomogeneously forming a ribbonlike structure as shown in Fig.2. The ribbon edges formed will have monolayered and multilayered steps at the edges. So, during the peeling off process it will exert vertical and lateral stresses on the ribbons. Due to applied vertical and lateral stresses during the pulling process, these ribbons will get dislocated vertically and laterally. It is know that π orbitals which are perpendicular to the graphite sheet are responsible for the electrical conductance along the sheet. It is also believed that the interlayer forces are the van der Waals’ forces. We believe that the π electrons not only take parts in conductivity, but also have to contribute substantially to the polarization cloud that gives the bonding between the layers. If the top layer is loosely held, then the π electrons of the loosely held top layers do not participate much in the bonding with the layer underneath. This makes the π electron more mobile leading to higher conductivity. Note: the carrier density does not change and it is only the mobility which increases thus leading to a higher conductivity.
Another important way in which the top layer may be more conducting could be due to an unavoidable crumpling of the top graphite sheet especially whenever such distortions are unrelaxed. This effectively introduces the next nearest neighbor hopping amplitude if one thinks of the π electron in terms of the tight binding approximation. The six isolated points in the Brillouin zone where the valence band and the conduction band touches for only the nearest neighbor hopping case is shown in Fig.1(d). With the introduction of the next nearest neighbor hopping expands these isolated points to a finite area as shown in Fig.1(e). This means larger density of low energy current carrying states at the Fermi level, resulting in an increased conductivity. In other words, the likeliness of having local unrelaxed crumpling of sheets is larger for the top layers and any crumpling automatically dopes the zero-gap semi-metal with added carriers.
The peeling of the layers were performed manually in an uncontrolled fashion. This can lead to different degrees of applied stress on different ribbons and cause different magnitude in the dislodgement. It can happen that two ribbons separated by distances but lying on top of the same graphite sheet can be dislodged in different proportions, i.e., the interlayer c-axis distance can be different. The one which has a larger c-axis distance will be more loosely held than the ribbon which has a lower c-axis value. The difference in conductance can be explained invoking the same arguments given for the first observation, i.e, the loosely held ribbons are more conducting than the tightly held layers. Thus in Fig.6 we observe that the two adjacent layers having almost a similar height separated by distance show different conductance. We can infer that the layers which show more conductance is a less tighter bond to the layers underneath or the layers might be crumpled. With our resolution we cannot check the crumpling of top layers. It needs more careful and higher resolution studies.
Similar conductivity/contrast landscape over monolayer graphite deposited over hexagonal Ni was seen earlier. The dominant mechanism of bonding of graphite over transition metal is the hybridization/mixing of carbon π electrons and the d electrons of the transition metals. The degree of hybridization can vary over the surface which can be due to domains on the graphite layers. Thus we believe that the contrast in the image will depend on the orientation of the graphite domain with respect to the Ni surface or vice versa. In our case, on the other hand there is hardly any hybridization between the π electrons with the adjacent layers. This is clear because there is no real band formation along the c axis. Hence the conductivity landscape observed by us on the graphene layers comes as a surprise. For the graphene case the mismatch due to domain orientation with respect to the adjacent layer will not play an important role in the conductivity as the π electrons among the layers are not hybridized. The main contrast we feel is due to the reasons mentioned above. Moreover the contrast observed by us using AFM is much stronger than the typical STM images.