Spin-dependent Seebeck effects in a graphene superlattice p–n junction with different shapes

Abstract

We theoretically calculate the spin-dependent transmission probability and spin Seebeck coefficient for a zigzag-edge graphene nanoribbon p–n junction with periodically attached stubs under a perpendicular magnetic field and a ferromagnetic insulator. By using the nonequilibrium Green’s function method combining with the tight-binding Hamiltonian, it is demonstrated that the spin-dependent transmission probability and spin Seebeck coefficient for two types of superlattices can be modulated by the potential drop, the magnetization strength, the number of periods of the superlattice, the strength of the perpendicular magnetic field, and the Anderson disorder strength. Interestingly, a metal to semiconductor transition occurs as the number of the superlattice for a crossed superlattice p–n junction increases, and its spin Seebeck coefficient is much larger than that for the T-shaped one around the zero Fermi energy. Furthermore, the spin Seebeck coefficient for crossed systems can be much pronounced and their maximum absolute value can reach 528 μV by choosing optimized parameters. Besides, the spin Seebeck coefficient for crossed p–n junction is strongly enhanced around the zero Fermi energy for a weak magnetic field. Our results provide theoretical references for modulating the thermoelectric properties of a graphene superlattice p–n junction by tuning its geometric structure and physical parameters.