Impurity spectra of graphene under electric and magnetic fields

Abstract

Using the coupled series expansion method developed in this paper, we have investigated the quantum behavior of Coulomb impurity states under external electric and magnetic fields in graphene. Under magnetic field, we have obtained an accurate full spectrum of the attractive and repulsive Coulomb impurities for both massless and massive Dirac electrons and have found that bound states can be tuned between in and out of the gap by Coulomb impurities and a magnetic field. When a linear radial electric field in combination with a magnetic field are applied, the energy levels of Coulomb impurity states experience intercrossing, and they disappear because of Klein tunneling as the electric field exceeds the magnetic field. The results are helpful in controlling Coulomb impurity states by external fields in graphene and the method proves to be an efficient way to obtain accurate solutions of the Dirac equation with various fields.