  Detecting conductance quantization in graphene nanostructures turned out more
challenging than expected. The observation of well-defined conductance plateaus
through graphene nanoconstrictions so far has only been accessible in the
highest quality suspended or h-BN encapsulated devices. However, reaching low
conductance quanta in zero magnetic field, is a delicate task even with such
ultra-high mobility devices. Here, we demonstrate a simple AFM-based
nanopatterning technique for defining graphene constrictions with high
precision (down to 10 nm width) and reduced edge-roughness (+/- 1 nm). The
patterning process is based on the in-plane mechanical cleavage of graphene by
the AFM tip, along its high symmetry crystallographic directions. As-defined,
narrow graphene constrictions with improved edge quality enable an
unprecedentedly robust QPC operation, allowing the observation of conductance
quantization even on standard $SiO_2/Si$ substrates, down to low conductance
quanta. Conductance plateaus, were observed at $ne^2/h$, evenly spaced by
$2e^2/h$ (corresponding to n = 3, 5, 7, 9, 11) in the absence of an external
magnetic field, while spaced by $e^2/h$ (n = 1, 2, 3, 4, 5, 6) in 8T magnetic
field.
