Tuning the pseudo-Zeeman splitting in graphene cones by magnetic field

• The size of level splitting in angular momentum channels is enhanced by introduction of a homogenous magnetic field.
• Pseudo-Zeeman splitting in graphene can be controlled by hydrogenic impurities.
• Pseudo-Zeeman splitting may be controlled by the strength of magnetic field in topological cones.

The effect of a homogeneous magnetic field on the energy spectrum of gapped graphene cones with long range charged Coulomb impurity is investigated within the framework of the perturbation theory. It is found that, besides lifting the degeneracy of angular momentum channels due to topological defects, the size of the corresponding splitting is enhanced by the introduction of a homogeneous magnetic field. This indicates that the level splitting may be controlled by the strength of a magnetic field in topological cones. Therefore, our results show that the magnetic field may be used as a tool to tune the pseudo-Zeeman splitting in graphene cones.