Biperiodic superlattices and transparent states in graphene

The transmission and transport properties of biperiodic graphene superlattices are studied theoretically. Special attention is paid to the so-called transparent states of biperiodic superlattices. A Dirac-like Hamiltonian is used to describe the charge carriers in graphene. The transfer matrix method and the Landauer–Büttiker formalism are implemented to obtain the transmittance and conductance, respectively. Similar results to those reported for Schrödinger electrons are obtained. However, in the case of Dirac electrons the splitted bands and the transparent states associated to the biperiodicity depend strongly on the angle of incidence as well as the character of the charge carriers. In fact, the dynamic of the splitted bands and transparent states is inverted for holes. The origin of transparent states is unveiled by obtaining an analytic expression for the transmittance. It is found that resonant transmission through single and double barriers gives rise to transparent states. Regarding the transport properties, it is possible to identify the fundamental changes caused by the biperiodicity. In particular, it is found a splitting, shifting, and diminishment of the conductance peaks with respect to the case of regular periodicity. This opens the door to corroborate experimentally the fundamental characteristics of biperiodic gated graphene superlattices through transport measurements.