The first excited state energy of strong coupled bound polaron in monolayer graphene

Properties of strong coupled polaron in monolayer graphene are discussed in the presence of the Coulomb interaction. The linear combination operator method and Lee-Low-Pine unitary transformation method are used to calculate the first exited state energy of the polaron for various values of the electron-phonon coupling. It is shown that the first exited state energy of the system has a linear relationship with the magnetic field strength, the cut-off wave number, the Coulomb bound parameter, the distance between the graphene and the substrate.