▎ 摘　　要

The polaron effects are investigated in the presence of a magnetic field based on the carrier-surface optical phonon coupling induced by the polar substrates under the graphene. We find that the energy gap is opened in the zero-energy Landau level due to the polaron effect. The magnitude of energy gap is consistent with recent experimental measurements. Moreover, the gap can be tuned by choosing the polarization of substrates and controlling the distance between graphene and polar substrate. The results obtained provide a possible explanation for the origin of energy gap opening and highlight the bandgap engineering of graphene on polar substrates. (C) 2015 AIP Publishing LLC.