Energy Spectra of the Graphene-based Fibonacci Superlattice Modulated by the Fermi Velocity Barriers

The one-dimensional superlattice (SL) based on a monolayer graphene modulated by the Fermi velocity barriers is considered. We assume that the rectangular barriers are arranged periodically along the SL chain. The energy spectra of the Weyl-Dirac quasi-electrons for this SL are calculated with the help of the transfer matrix method in the continuum model. The Fibonacci quasi-periodic modulation in graphene superlattices with the velocity barriers can be effectively realized by virtue of a difference in the velocity barrier values (no additional factor is needed). And this fact is true for a case of normal incidence of quasi-electrons on a lattice. In contrast to the case of other types of the graphene SL spectra studied reveal the periodic character over all the energy scale and the transmission coefficient doesn’t tend asymptotically to unity at rather large energies. The dependence of spectra on the Fermi velocity magnitude and on the external electrostatic potential as well as on the SL geometrical parameters (width of barriers and quantum wells) is analyzed. The obtained results can be used for applications in the graphene-based electronics.