Facile characterization of ripple domains on exfoliated graphene.

Ripples in graphene monolayers deposited on SiO(2)/Si wafer substrates were recently shown to give rise to friction anisotropy. High friction appears when the AFM tip slides in a direction perpendicular to the ripple crests and low friction when parallel. The direction of the ripple crest is, however, hard to determine as it is not visible in topographic images and requires elaborate measurements of friction as a function of angle. Here we report a simple method to characterize ripple crests by measuring the cantilever torsion signal while scanning in the non-conventional longitudinal direction (i.e., along the cantilever axis, as opposed to the usual friction measurement). The longitudinal torsion signal provides a much clearer ripple domain contrast than the conventional friction signal, while both signals show respective rotation angle dependences that can be explained using the torsion component of the normal reaction force exerted by the graphene ripples. We can also determine the ripple direction by comparing the contrast in torsion images obtained in longitudinal and lateral scans without sample rotation or complicated normalization.