Charge and spin currents in mesoscopic rings: Role of next nearest-neighbors Rashba spin–orbit coupling using the Green’s functions equation of motion technique

The electronic states of a mesoscopic ring are assessed using the Green functions approach and the equation of motion method. We put forward the Green’s function formalism to evaluate precisely persistent charge and spin currents in a ring exhibiting nearest-neighbors (NN) and next-nearest (NNN) neighbors Rashba spin–orbit interactions. Our present scheme circumvents direct diagonalization of the Hamiltonian, allowing to determine numerically persistent currents with both spin–orbit interactions simultaneously. Our results for the spin currents show that the NN Rashba interaction breaks the spin degeneracy producing a square-like shape; while the NNN Rashba interaction creates an energy-dependent splitting of the levels that generates a pattern of small peaks. The merging of both interactions rises a periodic squared-peaked pattern at half integer values of the quantum flux, which suggests the possibility of controlling the spin current magnitude and polarization by modulating the NNN Rashba parameter.