The effects of the magnetopolaron on the energy gap opening in graphene

The magnetopolaron is formed via electron-acoustic deformation phonon coupling in the presence of a magnetic field in monolayer graphene. We find that an energy gap (EG) is opened due to the electron-phonon coupling. Both linear and square-root forms for the dependence of the EG on the magnetic field are obtained, which are in agreement with experimental measurements. Furthermore, we suggest that the EG can be estimated through observing the variation of Fermi velocity in cyclotron resonance experiments. The relation of the EG with the Debye cut-off wavenumber is also discussed.