Thermoelectric properties of magnetic configurations of graphene-like nanoribbons in the presence of Rashba and spin-orbit interactions

In this paper we investigate the influence of spin-orbit interaction and two types of Rashba interaction (intrinsic and extrinsic) on magnetic and thermoelectric properties of graphene-like zigzag nanoribbons based on the honeycomb lattice. We utilize the Kane-Mele model with additional Rashba interaction terms. Magnetic structure is described by the electron-electron Coulomb repulsion reduced to the on-site interaction (Hubbard term) in the mean field approximation. We consider four types of magnetic configurations: ferromagnetic and antiferromagnetic with in-plane and out-of plane direction of magnetization. Firstly, we analyze the influence of extrinsic Rashba coupling on systems with negligible spin-orbit interaction, e.g. graphene of an appropriate substrate. Secondly, we discuss the interplay between spin-orbit and intrinsic Rashba interactions. This part is relevant to materials with significant spin-orbit coupling such as silicene and stanene.