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

May quasicrystals be good thermoelectric materials?

We present a theoretical analysis of quasicrystals (QCs) as potential thermoelectric materials. We consider a self-similar density of states model and extend the framework introduced in [G. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] to systems exhibiting correlated features in their electronic structure. We show that relatively high values of the thermoelectric figure of merit, ranging from 0.01 up to 1.6 at room temperature, may be expected for these systems. We compare our results with available experimental data on transport properties of QCs and suggest some potential candidates for thermoelectric applications

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

Exploiting quasiperiodic order in the design of optical devices

In this work we present a prospective study on the potential capabilities of optical devices based on Fibonacci dielectric multilayers. We perform a detailed analytical comparison of the linear optical response of periodic versus quasiperiodic multilayers. Based on this study we will suggest the use of hybrid-order devices, composed of both periodic and quasiperiodic subunits to design microcavities of practical interest, and we provide some illustrative examples. From our study we conclude that the inclusion of quasiperiodically ordered subunits substantially widens the possibilities of engineering modular optical structures

Tunnelling in quantum superlattices with variable lacunarity

Quantum fractal superlattices are microelectronic devices consisting of a series of thin layers of two semiconductor materials deposited alternately on each other over a substrate following the rules of construction of a fractal set, here, a symmetrical polyadic Cantor fractal. The scattering properties of electrons in these superlattices may be modeled by using that of quantum particles in piecewise constant potential wells. The twist plots representing the reflection coefficient as function of the lacunarity parameter show the appearance of black curves with perfectly transparent tunnelling which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for these reflection-less curves are derived using the transfer matrix method. Comparison with the numerical results show their good accuracy.Comment: 12 pages, 3 figure

Electronic transport in the Koch fractal lattice

In this work we extend the algebraic approach introduced in the context of general Fibonacci systems [E. Maciá and F. Domínguez-Adame, Phys. Rev. Lett. 76, 2957 (1996)] to analytically study the transmission coefficient of a subset of states in the fractal Koch lattice. We report on the existence of extended states whose transmission coefficients periodically oscillate as the Koch curve approaches its fractal limit

Three-Dimensional Effects on the Electronic Structure of Quasiperiodic Systems

We report on a theoreticl study of the electronic structure of quasiperiodic, quasi-one-dimensional systems where fully three dimensional interaction potentials are taken into account. In our approach, the actual physical potential acting upon the electrons is replaced by a set of nonlocal separable potentials, leading to an exactly solvable Schrodinger equation. By choosing an appropriate trial potential, we obtain a discrete set of algebraic equations that can be mapped onto a general tight-binding-like equation. We introduce a Fibonacci sequence either in the strength of the on-site potentials or in the nearest-neighbor distances, and we find numerically that these systems present a highly fragmented, self-similar electronic spectrum, which becomes singular continuous in the thermodynamical limit. In this way we extend the results obtained so far in one-dimensional models to the three-dimensional case. As an example of the application of the model we consider the chain polymer case.Comment: REVTeX 3.0, 19 pages, 6 figures (available upon request). To appear in Physica

Do quasicrystals follow Wiedemann-Franz's law?

In this work we present a theoretical study on the thermal and electrical conductivities of quasicrystals. By considering a realistic model for the spectral conductivity we derive closed analytical expressions for the transport coefficients which allow us to study the temperature dependence of the Lorenz ratio L( T) = κ_(e)(T)/ Tσ( T) at different temperature regimes. We conclude that quasicrystals closely follow Wiedemann- Franz's law over a wide temperature range

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]

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