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

• Tamm state, a homogeneous potential and a magneto-electric potential superlattice.
• Tamm states in anti-parallel potential superlattice are symmetrical about ky′.
• Tamm states in anti-parallel magnetic superlattice, symmetrical about E0E0 at ±Vs±Vs.
• Tamm states in combined magneto-electric potential superlattice have no symmetry.

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 ky′=0 at the same intensity of the homogeneous potential barrier (VsVs). 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 VsVs are symmetric to that at negative VsVs about the electron incident energy E0=0E0=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 ky′ or the electron incident energy whether at the same VsVs or at positive and negative VsVs.