The Energy Levels of a Shallow Impurity in Monolayer Graphene in a Perpendicular Magnetic Field

The energies of the ground 1S and the first three excited levels of 2S, 2P– and $$2{{P}^{ + }}$$ of a shallow impurity in graphene monolayer with an opened energy gap in a perpendicular magnetic field, are studied by a variational approach. The dependences of the energy of impurity levels on magnitude of the magnetic field are obtained for various values of the “thickness” parameter b of “softened” Coulomb potential. The ability to control the position of impurity energies and distance between them in graphene by changing the magnetic field opens possibilities for implementation of new schemes of coherent interaction of laser pulses with graphene systems.