Transport and localization in periodic and disordered graphene superlattices

We study the transport of low-energy charged quasiparticles in graphene superlattices created by applying either periodic or disordered smooth scalar potentials, which cause no intervalley scattering. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimum nonzero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). Owing to these features, such samples could be used as building blocks in tunable electronic circuits. It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Remarkable properties of the transmission have been found in graphene systems built of alternating p-n and n-p junctions. The mean transmission coefficient has anomalously narrow angular spectrum, practically independent of the amplitude of the fluctuations of the potential. To better understand the physical implications of the results presented here, most of these have been compared with the results for analogous electromagnetic wave systems. Along with similarities, a number of quite surprising differences have been found.