Unraveling quantum Hall breakdown in bilayer graphene with scanning gate microscopy.

Investigating the structure of quantized plateaus in the Hall conductance of graphene is a powerful way of probing its crystalline and electronic structure and will also help to establish whether graphene can be used as a robust standard of resistance for quantum metrology. We use low-temperature scanning gate microscopy to image the interplateau breakdown of the quantum Hall effect in an exfoliated bilayer graphene flake. Scanning gate images captured during breakdown exhibit intricate patterns where the conductance is strongly affected by the presence of the scanning probe tip. The maximum density and intensity of the tip-induced conductance perturbations occur at half-integer filling factors, midway between consecutive quantum Hall plateau, while the intensity of individual sites shows a strong dependence on tip-voltage. Our results are well-described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering in a network of saddle points separating localized states.