X-Ray Reflectivity of Fibonacci Multilayers

We have numerically computed the reflectivity of X-ray incident normally onto Fibonacci multilayers, and compared the results with those obtained in periodic approximant multilayers. The constituent layers are of low and high refractive indices with the same thickness. Whereas reflectivity of periodic approximant multilayers changes only slightly with increasing the number of layers, Fibonacci multilayers present a completely different behaviour. In particular, we have found a highly-fragmented and self-similar reflectivity pattern in Fibonacci systems. The behaviour of the fragmentation pattern on increasing the number of layers is quantitatively described using multifractal techniques. The paper ends with a brief discussion on possible practical applications of our results in the design of new X-ray devices.Comment: 8 pages, REVTeX 3.0, 3 figures available upon request from [email protected]. To appear in Physics Letters

Staggered and extreme localization of electron states in fractal space

We present exact analytical results revealing the existence of a countable infinity of unusual single particle states, which are localized with a multitude of localization lengths in a Vicsek fractal network with diamond shaped loops as the 'unit cells'. The family of localized states form clusters of increasing size, much in the sense of Aharonov-Bohm cages [J. Vidal et al., Phys. Rev. Lett. 81, 5888 (1998)], but now without a magnetic field. The length scale at which the localization effect for each of these states sets in can be uniquely predicted following a well defined prescription developed within the framework of real space renormalization group. The scheme allows an exact evaluation of the energy eigenvalue for every such state which is ensured to remain in the spectrum of the system even in the thermodynamic limit. In addition, we discuss the existence of a perfectly conducting state at the band center of this geometry and the influence of a uniform magnetic field threading each elementary plaquette of the lattice on its spectral properties. Of particular interest is the case of extreme localization of single particle states when the magnetic flux equals half the fundamental flux quantum.Comment: 9 pages, 8 figure

Dynamical phenomena in Fibonacci Semiconductor Superlattices

We present a detailed study of the dynamics of electronic wavepackets in Fibonacci semiconductor superlattices, both in flat band conditions and subject to homogeneous electric fields perpendicular to the layers. Coherent propagation of electrons is described by means of a scalar Hamiltonian using the effective-mass approximation. We have found that an initial Gaussian wavepacket is filtered selectively when passing through the superlattice. This means that only those components of the wavepacket whose wavenumber belong to allowed subminibands of the fractal-like energy spectrum can propagate over the entire superlattice. The Fourier pattern of the transmitted part of the wavepacket presents clear evidences of fractality reproducing those of the underlying energy spectrum. This phenomenon persists even in the presence of unintentional disorder due to growth imperfections. Finally, we have demonstrated that periodic coherent-field induced oscillations (Bloch oscillations), which we are able to observe in our simulations of periodic superlattices, are replaced in Fibonacci superlattices by more complex oscillations displaying quasiperiodic signatures, thus sheding more light onto the very peculiar nature of the electronic states in these systems.Comment: 7 pagex, RevTex, 5 Postscript figures. Physical Review B (in press

Fluorescence decay in aperiodic Frenkel lattices

We study motion and capture of excitons in self-similar linear systems in which interstitial traps are arranged according to an aperiodic sequence, focusing our attention on Fibonacci and Thue-Morse systems as canonical examples. The decay of the fluorescence intensity following a broadband pulse excitation is evaluated by solving the microscopic equations of motion of the Frenkel exciton problem. We find that the average decay is exponential and depends only on the concentration of traps and the trapping rate. In addition, we observe small-amplitude oscillations coming from the coupling between the low-lying mode and a few high-lying modes through the topology of the lattice. These oscillations are characteristic of each particular arrangement of traps and they are directly related to the Fourier transform of the underlying lattice. Our predictions can be then used to determine experimentally the ordering of traps.Comment: REVTeX 3.0 + 3PostScript Figures + epsf.sty (uuencoded). To appear in Physical Review

Anomalous optical absorption in a random system with scale-free disorder

We report on an anomalous behavior of the absorption spectrum in a one-dimensional lattice with long-range-correlated diagonal disorder with a power-like spectrum in the form S(k) ~ 1/k^A. These type of correlations give rise to a phase of extended states at the band center, provided A is larger than a critical value A_c. We show that for A < A_c the absorption spectrum is single-peaked, while an additional peak arises when A > A_c, signalling the occurrence of the Anderson transition. The peak is located slightly below the low-energy mobility edge, providing a unique spectroscopic tool to monitor the latter. We present qualitative arguments explaining this anomaly.Comment: 4 pages, 4 postscript figures, uses revtex

Environment effects on the electric conductivity of the DNA

We present a theoretical analysis of the environment effects on charge transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached to two ideal leads. Coupling of the DNA to the environment results in two effects: (i) localization of carrier functions due to the static disorder and (ii) phonon-induced scattering of the carrier between these localized states, resulting in hopping conductivity. A nonlinear Pauli master equation for populations of localized states is used to describe the hopping transport and calculate the electric current as a function of the applied bias. We demonstrate that, although the electronic gap in the density of states shrinks as the disorder increases, the voltage gap in the $I-V$ characteristics becomes wider. Simple physical explanation of this effect is provided.Comment: 8 pages, 2 figures, to appear in J. Phys.: Condens. Matte

Exciton Optical Absorption in Self-Similar Aperiodic Lattices

Exciton optical absorption in self-similar aperiodic one-dimensional systems is considered, focusing our attention on Thue-Morse and Fibonacci lattices as canonical examples. The absorption line shape is evaluated by solving the microscopic equations of motion of the Frenkel-exciton problem on the lattice, in which on-site energies take on two values, according to the Thue-Morse or Fibonacci sequences. Results are compared to those obtained in random lattices with the same stechiometry and size. We find that aperiodic order causes the occurrence of well-defined characteristic features in the absorption spectra which clearly differ from the case of random systems, indicating a most peculiar exciton dynamics. We successfully explain the obtained spectra in terms of the two-center problem. This allows us to establish the origin of all the absorption lines by considering the self-similar aperiodic lattices as composed of two-center blocks, within the same spirit of the renormalization group ideas.Comment: 16 pages in REVTeX 3.0. 2 figures on request to F. D-A ([email protected]

Long range correlations in DNA : scaling properties and charge transfer efficiency

We address the relation between long range correlations and charge transfer efficiency in aperiodic artificial or genomic DNA sequences. Coherent charge transfer through the HOMO states of the guanine nucleotide is studied using the transmission approach, and focus is made on how the sequence-dependent backscattering profile can be inferred from correlations between base pairs.Comment: Submitted to Phys. Rev. Let

Wave interactions in localizing media - a coin with many faces

A variety of heterogeneous potentials are capable of localizing linear non-interacting waves. In this work, we review different examples of heterogeneous localizing potentials which were realized in experiments. We then discuss the impact of nonlinearity induced by wave interactions, in particular its destructive effect on the localizing properties of the heterogeneous potentials.Comment: Review submitted to Intl. Journal of Bifurcation and Chaos Special Issue edited by G. Nicolis, M. Robnik, V. Rothos and Ch. Skokos 21 Pages, 8 Figure

Physical nature of critical wave functions in Fibonacci systems

We report on a new class of critical states in the energy spectrum of general Fibonacci systems. By introducing a transfer matrix renormalization technique, we prove that the charge distribution of these states spreads over the whole system, showing transport properties characteristic of electronic extended states. Our analytical method is a first step to find out the link between the spatial structure of these critical wave functions and the quasiperiodic order of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in Phys. Rev. Let