Coulomb impurity effects on the zero-Landau level splitting of graphene on polar substrates

We theoretically investigate the effects of the Coulomb impurity on the zero-Landau level splitting of graphene on different polar substrates basing on the Fröhlich polaron model, in which the polaron is formed due to the carriers-surface optical phonon coupling. We discuss the influence of Coulomb impurity on the zero-Landau level splitting in the case of weak and strong coupling limits. We find that the splitting energy can be varied in a large scale due to the Coulomb impurity, which provides the possible theoretical explanation for the experimental measurements regarding the energy gap opened and zero-Landau level splitting in Landau quantized graphene.