Manipulating quantum Hall edge channels in graphene through Scanning Gate Microscopy

We show evidence of the backscattering of quantum Hall edge channels in a narrow graphene Hall bar, induced by the gating effect of the conducting tip of a Scanning Gate Microscope, which we can position with nanometer precision. We show full control over the edge channels and are able, due to the spatial variation of the tip potential, to separate co-propagating edge channels in the Hall bar, creating junctions between regions of different charge carrier density, that have not been observed in devices based on top- or split-gates. The solution of the corresponding quantum scattering problem is presented to substantiate these results, and possible follow-up experiments are discussed.Comment: 10 pages, 12 figure