Graphene with Rashba spin-orbit interaction and coupling to a magnetic layer: Electron states localized at the domain wall

Abstract

Edge electron states localized at the magnetic domain wall in a graphene monolayer with Rashba spin-orbit interaction and coupled to a magnetic overlayer are studied analytically. It is shown that two one-dimensional bands of edge modes propagating along the domain wall emerge in the energy gap for each Dirac point, and the modes associated with different Dirac points K and K' are related by symmetry of the system. The coefficients describing decay of the corresponding wavefunctions with distance from the domain wall contain generally imaginary terms. Numerical results on the local spin density and on the total spin expected in the edge states characterized by the wavenumber ky are presented and discussed.