▎ 摘　　要

We study graphene nanoribbons theoretically in the presence of spatially varying magnetic fields produced, e.g., by nanomagnets. We show, both analytically and numerically, that an exceptionally large Rashba spin-orbit interaction of the order of 10 meV can be produced by a nonuniform magnetic field. As a consequence, helical modes exist in armchair nanoribbons that exhibit nearly perfect spin polarization and are robust against boundary defects. This result paves the way for realizing spin-filter devices in graphene nanoribbons in the temperature regime of a few kelvins. If a nanoribbons in the helical regime is in proximity contact to an s-wave superconductor, the nanoribbon can be tuned into a topological phase that sustains Majorana fermions. DOI: 10.1103/PhysRevX.3.011008