Spatial confinement, magnetic localization, and their interactions on massless Dirac fermions

Understanding different approaches to confining massless Dirac fermions in graphene is of keen interest to researchers; it is also a central problem in making electronic devices based on graphene. Here, we studied spatial confinement, magnetic localization, and their interactions on massless Dirac fermions in an angled graphene wedge formed by two linear graphene p-n boundaries with an angle similar to 34 degrees. Using scanning tunneling microscopy, we visualized quasibound states temporarily confined in the studied graphene wedge. Large perpendicular magnetic fields condensed the massless Dirac fermions in the graphene wedge into Landau levels (LLs). The spatial confinement of the wedge affects the Landau quantization, which enables us to experimentally measure the spatial extent of the wave functions of the LLs. The magnetic fields induce a sudden and large increase in energy of the quasibound states because of a pi Berry phase jump of the massless Dirac fermions in graphene. Such behavior is the hallmark of the "Klein tunneling" in graphene. Our experiment demonstrated that the angled wedge is a unique system with the critical magnetic fields for the n Berry phase jump depending on the distance from the summit of the wedge.