Electron beam splitting effect with crossed zigzag graphene nanoribbons in high-spin metallic states

Here we analyze the electron transport properties of a device formed of two crossed graphene nanoribbons with zigzag edges (ZGNRs) in a spin state with total magnetization different from zero. While the ground state of ZGNRs has been shown to display antiferromagnetic ordering between the electrons at the edges, for wide ZGNRs--where the localized spin states at the edges are decoupled and the exchange interaction is close to zero--, in presence of relatively small magnetic fields, the ferromagnetic (FM) spin configuration can in fact become the state of lowest energy due to the Zeeman effect. In these terms, by comparing the total energy of a periodic ZGNR as a function of the magnetization per unit cell we obtain the FM-like solution of lowest energy for the perfect ribbon, the corresponding FM-like configuration of lowest energy for the four-terminal device formed of crossed ZGNRs, and the critical magnetic field needed to excite the system to this spin configuration. By performing transport calculations, we analyze the role of the distance between layers and the crossing angle of this device in the electrical conductance, at small gate voltages. The problem is approached employing the mean-field Hubbard Hamiltonian in combination with non-equilibrium Green's functions. We find that ZGNR devices subject to transverse magnetic fields may acquire a high-spin configuration that ensures a metallic response and tunable beam splitting properties, making this setting promising for studying electron quantum optics with single-electron excitations.