On the Nature of Electronic Wave Functions in One-Dimensional Self-Similar and Quasiperiodic Systems

Maciá, Enrique

doi:10.1155/2014/165943

Cited by 29 publications

(31 citation statements)

References 96 publications

(149 reference statements)

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“…In particular, the variation of the Landauer conductance as a function of the chemical bonding strength parameter A agrees with the reported sensitivity of the electrical transport properties of most icosahedral quasicrystalline alloys to di¤erent stoichiometric compositions. [53] The above well-known results concerning E resonant states belonging to the Fibonacci QC spectrum, [10,42] can be properly extended to all members of the precious means based BACs family. As a suitable example, let us start with the silver mean based QC.…”

Section: Transport Properties Of Resonant Statesmentioning

confidence: 89%

“…This feature properly distinguishes the BACs studied in this work from both the purely geometric on-site (i.e., t k;k 1 1, 8k) and the chemically unrealistic transfer (i.e., V k 0, 8k) models, which have been widely considered in the physical and mathematical literature during the last three decades. [4,10,[36][37][38] After Eq. (2) the wave function amplitudes can be recursively obtained from the matrix expression 0…”

Section: General Binary Aperiodic Crystals: a Unified Treatmentmentioning

confidence: 99%

“…To this end, we will zoom out the considered spatial scale, going from the nearest-neighbors scale related to the triplet level description all the way up to the entire lattice size scale. To achieve this goal, we will rewrite the global transfer matrix M N (E) of any given BAC in terms of just two block matrices R (n;m) A and R (n;m) B in the form, [10,[42][43][44] Table II clearly indicates that the topological order present in the original atomic lattice is preserved by the block matrices sequence appearing in Eq. (8).…”

Section: Local Transfer Matrices Classi…cationmentioning

confidence: 99%

“…Accordingly, the choice of appropriate elemental block matrices obeying certain self-similar schemes can be regarded as an e¤ective renormalization of the original local transfer matrices sequence. [10,42] In fact, from a physical point of view these matrices respectively describe the electron dynamics through the minimal atomic clusters in terms of which the entire BAC can be decomposed via an exact de ‡ation process. For instance, in the case of a Fibonacci QC these atomic clusters are BA and BAA.…”

Section: Local Transfer Matrices Classi…cationmentioning

confidence: 99%

“…1. [8][9][10][11][12][13] In the top panel chart we provide a graphical classi…cation scheme of aperiodic systems based on the nature of their di¤raction spectra (in abscissas) and their energy spectra (in ordinates), respectively. In this way, the old-fashioned classi…cation scheme based on the periodic-amorphous dichotomy is replaced by a much richer one, including nine di¤erent entries.…”

Section: Introductionmentioning

confidence: 99%

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Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Maciá

2017

Annalen der Physik

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A spectral classi…cation of general one-dimensional binary aperiodic crystals (BACs) based on both their di¤raction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth-order energy spectrum main features for BACs belonging to di¤erent spectral classes, including Fibonacci-class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed-type Hamiltonians which include both diagonal and o¤-diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation e¤ects present in the underlying lattice is introduced.Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which de…nes the basic anatomy of the zeroth-order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci-class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for speci…c particular choices of the corresponding model parameters only. The transmission coe¢ cient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.

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Section: Transport Properties Of Resonant Statesmentioning

confidence: 89%

Section: General Binary Aperiodic Crystals: a Unified Treatmentmentioning

confidence: 99%

Section: Local Transfer Matrices Classi…cationmentioning

confidence: 99%

Section: Local Transfer Matrices Classi…cationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Maciá

2017

Annalen der Physik

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Ballistic conduction in macroscopic non‐periodic lattices

Wang

García

Sánchez

et al. 2015

Physica Status Solidi (b)

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Phone number: þ52 55 5622 4634, Fax number: þ52 55 5616 1251In this paper, the dc electronic transport at zero temperature in aperiodic systems with macroscopic length is studied by using a real-space renormalization plus convolution method developed for the Kubo-Greenwood formula within the tight-binding formalism. We analytically prove the existence of transparent states in several generalized Fibonacci lattices, as well as in segmented linear chains, where they always appear if the number of bonds in each segment is even, regardless the ordering of segments. For two-dimensional square-lattice tapes with a periodic or non-periodic Fanoimpurity plane, we found a novel ballistic transport state in the dc conductance spectra.

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Clustering resonance effects in the electronic energy spectrum of tridiagonal Fibonacci quasicrystals

Maciá

2017

Phys. Status Solidi B

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In this work, we show that the fundamental structure of the electronic energy spectrum of binary Fibonacci quasicrystals can be decomposed in terms of two main contributions, stemming from two related characteristic symmetries. The algebraic approach, we introduce allows us for a unified and systematic description of the energy spectrum finer structure details in terms of block matrices commutators properties, within the framework of a renormalization approach based on transfer matrices. Close analytical expressions can be explicitly obtained by exploiting some algebraic properties of these blocks commutators. In particular, the overall main features of the electronic energy spectrum structure are related to the roots of a series of polynomials of the form pFjfalse(Efalse), where the subscript denotes the degree of the polynomial, which is given by a Fibonacci number Fj. These polynomials, in turn, are derived in a systematic way from commutators involving progressively longer palindromic fundamental blocks containing two types of basic renormalized matrices. In this way, we can classify the resonance energies defining the different fragmentation patterns of the energy spectrum on the basis of purely algebraic criteria. The transmission coefficient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the system length. The obtained results significantly contribute to gain a better understanding of the symmetry principles governing the fragmentation process leading to the characteristic nested structure of the energy spectrum.

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On the Nature of Electronic Wave Functions in One-Dimensional Self-Similar and Quasiperiodic Systems

Cited by 29 publications

References 96 publications

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Ballistic conduction in macroscopic non‐periodic lattices

Clustering resonance effects in the electronic energy spectrum of tridiagonal Fibonacci quasicrystals

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