Non-conventional Fermi velocity graphene superlattices

The transmission and transport properties of non-conventional Fermi velocity graphene superlattices (FVGSLs) are studied. Arithmetic, regular and random distributions of the Fermi velocity barriers are assessed. A velocity position-dependent Dirac-like Hamiltonian is used to describe the charge carriers. The transfer matrix method and the Landauer-Büttiker formalism are implemented to obtain the transmission and the integrated transmission (conductance) at zero temperature. We find that arithmetic FVGSLs show peculiar transport characteristics as compared to regular and random FVGSLs. In particular, the arithmetic profile eliminates the regular and irregular oscillations of the integrated transmission typical of regular and random FVGSLs. More importantly, arithmetic FVGSLs keep the integrated transmission around the same value regardless of the size of the system, presenting even an increase (crossover) with the size of the system for large Fermi velocity ratios. This contrasts with the systematic reduction of the integrated transmission with the size of the system for regular and random FVGSLs. We delve into the possible causes of the crossover of the integrated transmission for arithmetic FVGSLs.