Magnetic edge states in graphene.

We theoretically study the magnetic edge states of the Dirac fermions in graphene, formed along the boundary between the two domains in a spatially nonuniform magnetic field, B$_{0}$ in one domain and B$_{1}$ in the other domain, in the quantum Hall regime. The energy spectra of the magnetic edge states depend on whether B$_{0}$ is parallel or antiparallel to B$_{1}$. For the parallel case, the n=0 magnetic edge states are dispersionless, while they split into electron-like and hole-like levels for the antiparallel case. Here, n is the graphene Landau level index. These features are attributed to the coupling between the pseudo-spin of the magnetic edge states and the direction of the external magnetic field. We also study the modification of the energy spectra when the finite Zeeman spin splitting or an electrostatic step-like potential is considered. An Aharonov-Bohm interferometry, which can identify the existence of the magnetic edge states, is suggested for experimental study.