Surface electrostatic potentials in carbon nanotubes and graphene membranes investigated with electron holography

We used low-voltage transmission electron holography to probe surface electrostatic potentials in graphene membranes and carbon nanotubes, as the number of graphenes varies. Further, we measured the phase shift induced by an individual graphene, and mapped the phase shift variation throughout a whole few-graphene-crystal as a function of the local number of layers. We found a size/surface effect as the ratio between the surface and the total number of atoms increases for an individual nanotube or graphene membrane. This surface phase term can be related to a fine electrostatic potentials redistributions occurring at the outer layers in carbon nanotubes and graphene membranes.