Scanning gate microscopy in graphene nanostructures

The conductance of graphene nanoribbons and nanoconstrictions under the effect a scanning gate microscopy tip is systematically studied. Using scattering approach for noninvasive probes, first- second-order corrections caused by potential disturbance are expressed explicitly in terms states unperturbed structure. Numerical calculations confirm perturbative results, showing that term prevails plateaus, exhibiting universal scaling law armchair strips. For stronger tips, at specific probe widths strengths beyond regime, reveal appearance resonances originated from trapped below tip. zero-transverse-energy mode an metallic strip shown to be insensitive long-range electrostatic probe. defined on strip, allows get insight into breakdown quantization. first-order correction generically dominates low strength, while Fermi energies associated with faint becomes dominant relatively small strengths. In accordance spatial dependence partial local density states, largest occurs central part constriction, close edges. Nanoribbons zigzag edges exhibit similar response as case nanostructures, except when intervalley coupling induced destroys chiral edge states.