Direction-dependent tunneling through nanostructured magnetic barriers in graphene

Abstract

We evaluate the transmission through magnetic barriers in graphene-based nanostructures. Several particular cases are considered: a magnetic step, single and double barriers, and $\ensuremath{\delta}$-function barriers. A separate class of magnetic-barrier structures are those with inhomogeneous magnetic-field profiles, such that the average magnetic field vanishes, which can be realized by nanostructured ferromagnetic stripes placed on top of the graphene layer. Quantum bound states that are localized near or in the barrier are predicted for a magnetic step and some structures with finite-width barriers but none for $\ensuremath{\delta}$-function barriers. When a bound state is localized close to the barrier edge, it has a nonzero velocity parallel to this edge. The transmission depends strongly on the direction of the incident electron or hole wave vector and gives the possibility to construct a direction-dependent wave vector filter. In general, the resonant structure of the transmission is significantly more pronounced for (Dirac) electrons with linear spectrum than for the usual electrons with a parabolic spectrum.