Magnetoconductivity in quasiperiodic graphene superlattices

Abstract

The magnetoconductivity in Fibonacci graphene superlattices is investigated in a perpendicular magnetic field B. It was shown that the B-dependence of the diffusive conductivity exhibits a complicated oscillatory behavior whose characteristics cannot be associated with Weiss oscillations, but rather with Shubnikov-de Haas ones. The absense of Weiss oscillations is attributed to the existence of two incommensurate periods in Fibonacci superlattices. It was also found that the quasiperiodicity of the structure leads to a renormalization of the Fermi velocity vF of graphene. Our calculations revealed that, for weak B, the dc Hall conductivity σyx exhibits well defined and robust plateaux, where it takes the unexpected values ± 4 e2/ ℏ(2 N+ 1 ) , indicating that the half-integer quantum Hall effect does not occur in the considered structure. It was finally shown that σyx displays self-similarity for magnetic fields related by τ2 and τ4, where τ is the golden mean.