Frequency dependence of the Hall-potential distribution in quantum Hall systems: Roles of edge channels and current contacts

The spatial dependence of the Hall potential induced in a two-dimensional electron system (2DES) by AC source-drain voltage is studied theoretically in the incoherent linear transport in the strong-magnetic-field regime. The local capacitance approximation is employed in which the potential at each point of the 2DES is proportional to the induced charge at the same point. It is shown that the frequency dependence of the induced charge distribution is described by three time constants, τe for transport through an edge channel of the electron injected from a current contact, τeb for transition between the edge channel and the bulk state, and τb for diffusion into the bulk, which are quite different in magnitude: τe≪τeb≪τb in the quantum Hall regime of a typical sample. These three time constants also determine how the Hall potential evolves in the 2DES after the source-drain voltage is turned on. Calculated two-dimensional distribution of the Hall potential as a function of the frequency reveals that the Hall potential develops by penetrating into the bulk from source and drain contacts as well as from the edge channel.