Noninvasive charge sensing of graphene in quantum Hall regime with scanning tunneling microscopy

Under strong magnetic field, electrons in mono-layer graphene form highly degenerate Landau levels, hence the strongly enhancement of electron-electron interaction. As a result, fractional charge excitation appears and uniform electron liquid becomes unstable which gives rise to exotic charge order phases such as Wigner crystal, bubble, and stripe phase. Although evidence of fractional excitation has been found by various experimental techniques and strong indications of exotic charge orders have been revealed by transport anomalies, a noninvasive probe with spatial resolution of sub-magnetic length that is capable of imaging fractional charges or exotic charge orders is still lacking. Here, we map the intrinsic compressibility and electrostatic potential of graphene in quantum Hall regime using scanning tunneling microscopy. We fabricate double-layer graphene devices which consist of two mono-layer graphene separated by a thin hBN flake. By controlling the total charge density and inter-layer bias potential, we are able to use the top graphene layer as a sensor layer and probe the intrinsic properties of the second graphene layer. This method can potentially become a universal noninvasive charge sensing technique.