Magnetoconductivity in quasiperiodic graphene superlattices

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 $$v_{F}$$ v F of graphene. Our calculations revealed that, for weak B, the dc Hall conductivity $$\sigma _{yx}$$ σ yx exhibits well defined and robust plateaux, where it takes the unexpected values $$\pm 4e^{2}/\hslash \left( 2N+1\right) $$ ± 4 e 2 / ℏ 2 N + 1 , indicating that the half-integer quantum Hall effect does not occur in the considered structure. It was finally shown that $$\sigma _{yx}$$ σ yx displays self-similarity for magnetic fields related by $$\tau ^{2}$$ τ 2 and $$\tau ^{4}$$ τ 4 , where $$\tau $$ τ is the golden mean.