Disappearance of the Dirac cone in silicene due to the presence of an electric field

Using the two-dimensional ionic Hubbard model as a simple basis for describing the electronic structure of silicene in the presence of an electric field induced by the substrate, we use the coherent-potential approximation to calculate the zero-temperature phase diagram and the associated spectral function at half filling. We find that any degree of symmetry-breaking induced by the electric field causes the silicene structure to lose its Dirac fermion characteristics, thus providing a simple mechanism for the disappearance of the Dirac cone.