Electronic properties of bilayer and multilayer graphene

We study the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack. The simplicity of the model allows for an easy implementation of the coherent-potential approximation and some analytical results. Within the model we compute the self-energies, the density of states, and the spectral functions. Moreover, we obtain the frequency and temperature dependence of the conductivity as well as the dc conductivity. The c-axis response is unconventional in the sense that impurities increase the response for low enough doping. We also study the problem of impurities in the biased graphene bilayer.