RESUMO
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 [Formula: see text] of graphene. Our calculations revealed that, for weak B, the dc Hall conductivity [Formula: see text] exhibits well defined and robust plateaux, where it takes the unexpected values [Formula: see text], indicating that the half-integer quantum Hall effect does not occur in the considered structure. It was finally shown that [Formula: see text] displays self-similarity for magnetic fields related by [Formula: see text] and [Formula: see text], where [Formula: see text] is the golden mean.
RESUMO
We demonstrate that the band structure of a photonic crystal consisting of alternating layers of right-handed material (RHM) and left-handed material (LHM) can exhibit two types of zero- n[over ] gaps of zero width. It is shown that each type has an associated null-gap condition which determines the scaling properties of the frequency nu(0) at which the corresponding null gap occurs. Specifically, while scaling in the layer thicknesses does not modify the value of the frequency nu(0) determined by one of these conditions, the frequency nu(0) associated with the other one does not exhibit such a scaling behavior. We have also shown that near the touching point nu(0) (for both types of null gaps) and around the center of the Brillouin zone, the dispersion curves exhibit a linear dependence on the Bloch wave vector k . As a consequence, the corresponding density of states and group velocity are practically flat as functions of k in the neighborhood of k=0 . Another interesting property of the considered structure is that an electromagnetic wave with frequency nu(0) can be transmitted through a finite RHM-LHM photonic crystal without any change in amplitude and phase.
RESUMO
Within the Maxwell framework and using a transfer-matrix technique we have determined a general equation which governs the photonic band structure and the density of states of one-dimensional superlattices composed of two alternate layers characterized by different refractive indexes, which may take on positive as well as negative values. Besides the usual well-known results, we have found null-gap points for commensurate values of the optical path lengths of each layer. Furthermore, we have been able to characterize non-Bragg gaps that show up in frequency regions in which the average refractive index is null.