Enrique Maciá

The role of aperiodic order in science and technology

In this work we consider the role of aperiodic order in different domains of science and technology from an interdisciplinary approach. To start with, we introduce some general classification schemes for aperiodic arrangements of matter. Afterwards, we review the main physical properties and possible applications of quasiperiodic crystals. Several conceptual links between quasiperiodic crystals and the hierarchical structure of biopolymers are then discussed in connection with the charge transfer properties of both biological and synthetic DNA chains. The widespread presence of Fibonacci numbers and the golden mean in different physical contexts is also discussed. Promising technological applications of aperiodic systems are finally reviewed by considering both current and potential applications. In particular, we analyse the capability of exploiting aperiodic order in the design of novel devices based on semiconductor heterostructures and dielectric multilayers.

Exploiting aperiodic designs in nanophotonic devices

In this work we consider the role of aperiodic order-order without periodicity-in the design of different optical devices in one, two and three dimensions. To this end, we will first study devices based on aperiodic multilayered structures. In many instances the recourse to Fibonacci, Thue-Morse or fractal arrangements of layers results in improved optical properties compared with their periodic counterparts. On this basis, the possibility of constructing optical devices based on a modular design of the multilayered structure, where periodic and quasiperiodic subunits are properly mixed, is analyzed, illustrating how this additional degree of freedom enhances the optical performance in some specific applications. This line of thought can be naturally extended to aperiodic arrangements of optical elements, such as nanospheres or dielectric rods in the plane, as well as to three-dimensional photonic quasicrystals based on polymer materials. In this way, plentiful possibilities for new tailored materials naturally appear, generally following suitable optimization algorithms. Then, we present a detailed discussion on the physical properties supporting the preferential use of aperiodic devices in a number of optical applications, opening new avenues for technological innovation. Finally we suggest some related emerging topics that deserve some attention in the years to come.

Optical engineering with Fibonacci dielectric multilayers

We study the resonant transmission of light through Fibonacci dielectric multilayers (FDM). Making use of a transfer matrix renormalization technique [E. Macia and F. Dominguez-Adame, Phys. Rev. Lett. 76, 2957 (1996)] we obtain closed analytical expressions for the transmission coefficient under arbitrary incidence angle conditions. We analyze the relationship between the resonant wavelengths and the quasiperiodic structure of the substrate, suggesting the potential use of arrays containing FDMs of different sizes in the design of optical microcavities.

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 critical wave functions and their related transport properties. PACS numbers: 71.23.Ft, 61.44.‐n The notion of critical wave function (CWF) has evolved continuously since its introduction in the study of aperiodic systems [1], leading to a somewhat confusing situation. For instance, references to self-similar, chaotic, quasiperiodic, latticelike, or quasilocalized CWFs can be found in the literature depending on the different criteria adopted to characterize them [2‐6]. Generally speaking, CWFs exhibit a rather involved oscillatory behavior, displaying strong spatial fluctuations which show distinctive self-similar features in some instances. As a consequence, the notion of an envelope function, which has been most fruitful in the study of both extended and localized states, is mathematically ill-defined in the case of CWFs, and other approaches are required to properly describe them and to understand their structure. Most interestingly, the possible existence of extended states in several kinds of aperiodic systems, including both quasiperiodic [7 ‐ 10] and nonquasiperiodic ones [4,11], has been discussed in the last few years spurring the interest on the precise nature of CWFs and their role in the physics of aperiodic systems. From a rigorous mathematical point of view the nature of a state is uniquely determined by the measure of the spectrum to which it belongs. In this way, since it has been proven that Fibonacci lattices have purely singular continuous energy spectra [12], we must conclude that the associated electronic states cannot be, strictly speaking, extended in the Bloch’s sense. This result holds for other aperiodic lattices (Thue-Morse, period doubling) as well [13], and it may be a general property of the spectra of self-similar aperiodic systems [14]. On the other side, from a physical viewpoint, the states can be classified according to their transport properties which, in turn, are determined by the spatial distribution of the wave function amplitudes (charge distribution). Thus, conducting, crystalline systems are described by periodic Bloch states, whereas insulating systems are described by exponentially decaying wave functions corresponding to localized states. In this sense, since the amplitudes of CWFs in a Fibonacci lattice do not tend to zero at infinity but are bounded below throughout the system [15], one may expect their physical behavior to be more similar to that corresponding to extended states than to localized ones. In this Letter we are going to show analytically that a subset of the CWFs belonging to general Fibonacci systems are extended from a physical point of view. This result widens the notion of extended wave function to include electronic states which are not Bloch functions, and it is a relevant first step to clarify the precise manner in which the quasiperiodic order of Fibonacci systems influences their transport properties [16]. To this end we present, in the first place, a new renormalization approach opening, in a natural way, an algebraic formalism which allows us to give a detailed analytical account of the transport properties of CWFs for certain particular values of the energy. In the second place, we study the relationship between the spatial structure of CWFs and their transport properties, showing that self-similar wave functions are those exhibiting higher transmission coefficients in finite Fibonacci systems. The formalism we are going to introduce is based on the transfer matrix technique, where the solution of the Schrodinger equation is obtained by means of a product of 2 3 2 matrices. Real-space renormalization group approaches, based on decimation schemes, have proved themselves very successful in order to numerically obtain

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 highest occupied molecular orbital states of the guanine nucleotide is studied using the transmission approach, and the focus is on how the sequence-dependent backscattering profile can be inferred from correlations between base pairs.

Backbone-induced effects in the charge transport efficiency of synthetic DNA molecules

We report on a theoretical study pointing out the fundamental role of the backbone energetics in the charge transfer efficiency of polyG–polyC and polyA–polyT chains. The double-strand DNA (ds-DNA) molecules are modelled in terms of a single channel effective Hamiltonian. By introducing a two-step renormalization scheme analytical results for the energy spectrum and transmission coefficient are derived, and current–voltage characteristics are numerically investigated. Significant modulations of the main I–V features (voltage threshold, current amplitude) are reported and their physical origin is traced back to backbone-induced electronic effects. These results open new perspectives for experimental work aimed at controlling the charge transfer efficiency in nanodevices based on synthetic DNA.

The role of phosphorus in chemical evolution

In this tutorial review we consider the role of phosphorus and its compounds within the context of chemical evolution in galaxies. Following an interdisciplinary approach we first discuss the position of P among the main biogenic elements by considering its relevance in most essential biochemical functions as well as its peculiar chemistry under different physicochemical conditions. Then we review the phosphorus distribution in different cosmic sites, such as terrestrial planets, interplanetary dust particles, cometary dust, planetary atmospheres and the interstellar medium (ISM). In this way we realize that this element is both scarce and ubiquitous in the universe. These features can be related to the complex nucleosynthesis of P nuclide in the cores of massive stars under explosive conditions favouring a wide distribution of this element through the ISM, where it would be ready to react with other available atoms. A general tendency towards more oxidized phosphorus compounds is clearly appreciated as chemical evolution proceeds from circumstellar and ISM materials to protoplanetary and planetary condensed matter phases. To conclude we discuss some possible routes allowing for the incorporation of phosphorus compounds of prebiotic interest during the earlier stages of solar system formation.

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.

ELECTRONIC TRANSPORT AND THERMOPOWER IN APERIODIC DNA SEQUENCES

A detailed study of charge transport properties of synthetic and genomic DNA sequences is reported. Genomic sequences of the Chromosome 22, λ-bacteriophage, and D1s80 genes of Human and Pygmy chimpanzee are considered in this work, and compared with both periodic and quasiperiodic (Fibonacci) sequences of nucleotides. Charge transfer efficiency is compared for all these different sequences, and large variations in charge transfer efficiency, stemming from sequence-dependent effects, are reported. In addition, basic characteristics of tunneling currents, including contact effects, are described. Finally, the thermoelectric power of nucleobases connected in between metallic contacts at different temperatures is presented.

Dynamical phenomena in Fibonacci semiconductor superlattices

We present a detailed study of the dynamics of electronic wave packets 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 wave packet is filtered selectively when passing through the superlattice. This means that only those components of the wave packer whose wave numbers 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 wave packet 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-induced defects. 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 shedding more light onto the very peculiar nature of the electronic states in these systems.