Theory of snake states in graphene

We study the dynamics of the electrons in a nonuniform magnetic field applied perpendicular to a graphene sheet in the low-energy limit when the excitation states can be described by a Dirac-type Hamiltonian. Compared to two-dimensional electron gas systems, we show that snake states in graphene exhibit peculiar properties related to the underlying dynamics of the Dirac fermions. The current carried by snake states is locally uncompensated, leading to a current inhomogeneity in the ground state.