Low dimensional systems, such as atomically thin materials and material interfaces, offer a rich ground to discover new types of electronic states. Spatially resolved electrical probes provide direct access to these electronic states on the mesoscopic scale, complementing conventional transport techniques. In this talk, I will present two comprehensive studies on low dimensional electronic states employing Microwave Impedance Microscopy (MIM), a scanning probe technique that senses materials’ capacitance and conductivity on the nanoscale.

        The first study examines the canonical “edge state” picture of the quantum Hall (QH) effect in graphene, by combining MIM measurement which probes the filling of Landau levels (LL) in graphene bulk with edge-sensitive quantum transport. To our surprise, we find an unconventional edge-bulk correlation in graphene devices: the QH transport plateaus occur before the bulk Landau levels are completely filled. We explain this by analyzing complex edge-state configuration induced by electrostatic gating near the sharp graphene edges.

        In the second study, we investigate metallic domain walls in a unique all-in-all-out magnetic insulator, Nd2Ir2O7. Through a combined study of MIM, transport, and X-ray micro-diffraction, we conclusively show that metallic states emerge at the magnetic domain walls when the all-in-all-out magnetic order forms with a concomitant metal-insulator transition occurring in the bulk. This represent a new type of interface conduction in a both chemically and structurally homogeneous material.