Charge and spin transport at the quantum Hall edge of graphene

Landau level bending near the edge of graphene, described using a 2d Dirac equation, provides a microscopic framework for understanding the quantum Hall effect (QHE) in this material. We review properties of the QHE edge states in graphene, with emphasis on the novel phenomena that arise due to the Dirac character of electronic states. A method of mapping out the dispersion of edge states using scanning tunneling probes is proposed. The Zeeman splitting of Landau levels is shown to create a particularly interesting situation around the Dirac point, where it gives rise to counter-circulating modes with opposite spin. These chiral spin modes lead to a rich variety of spin transport phenomena, including the spin Hall effect, spin filtering and injection, and electric detection of spin current. The estimated Zeeman spin gap, enhanced by exchange, of a few hundred Kelvin, makes graphene an attractive system for spintronics. Comparison to recent transport measurements near ν=0 is presented.