Tamm states in graphene-based different combined magneto-electric superlattice heterostructures

Tamm states localized at the interface between a homogeneous potential barrier and a combined magneto-electric potential barriers superlattice in monolayer graphene have been theoretically investigated. The results show that the symmetries of Tamm states are different when the components of the superlattice are different. When the single unit of the superlattice consists of double anti-parallel potential barriers and two gaps, Tamm states present symmetry about momentum wave vector k_y^′=0 at the same intensity of the homogeneous potential barrier (V_s). When the single unit of the superlattice consists of double anti-parallel magnetic potential barriers and two gaps, it demonstrates that Tamm states at positive V_s are symmetric to that at negative V_s about the electron incident energy E₀=0. When the single unit of the superlattice consists of double anti-parallel combined magneto-electric potential barriers, the band gap at Dirac point is opened, Tamm states exhibit no symmetry about k_y^′ or the electron incident energy whether at the same V_s or at positive and negative V_s.