  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 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.
