Impurity effects and bandgap-closing in massive Dirac systems

We investigate the effects in the spectral properties of a massive Dirac system of the dynamical renormalization induce by disorder/impurity scattering within the self-consistent Born approximation. We show how that these effects leads to a remarkable closing of the bandgap edge. Above a critical value $U_c$ of the impurity scattering the gap eventually closes, giving rise a finite density of states at zero energy. We show that the bandgap closing stems from the quasi-particle dynamical renormalization and it is not associated with the vanishing of the effective massive term. Incoherent processes are fundamental to describe such physics.