Renormalization approach to the electronic localization and transport in macroscopic generalized Fibonacci lattices

Sánchez, Fernando; Sánchez, Vicenta; Wang, Chumín

doi:10.1016/j.jnoncrysol.2016.07.031

Cited by 15 publications

(12 citation statements)

References 29 publications

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“…This has developed into a cool topic [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], which besides is underpinned by remarkable mathematical properties [57]. This confirms that the deterministic aperiodic nanostructures is a highly interdisciplinary and fascinating research field, conceptually rooted in several branches of mathematics.…”

Section: Introductionmentioning

confidence: 76%

Lempel-Ziv Complexity of Photonic Quasicrystals

Monzón¹,

Felipe²,

Sánchez-Soto

2017

Preprint

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The properties of photonic quasicrystals ultimate rely on their inherent long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. We use the Lempel-Ziv measure, a basic tool for information theoretic problems, to characterize the complexity of the specific structure under consideration. Using the generalized Fibonacci quasicrystals as our thread, we adress the relation between the optical response and the associated complexity.

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Section: Introductionmentioning

confidence: 76%

Lempel-Ziv Complexity of Photonic Quasicrystals

Monzón¹,

Felipe²,

Sánchez-Soto

2017

Preprint

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“…[52] In obtaining Eq. (26) one assumes the BAC is sandwiched between two periodic chains (playing the role of contacts), each one with on-site energy " 0 and transfer integral t 0 , so that their dispersion relation is given by E = " 0 + 2t 0 cos .…”

Section: Transport Properties Of Resonant Statesmentioning

confidence: 99%

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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“…(42) to get (rR 2 ) 2 = U 1 (z)rR 2 − U 0 (z)I = trF 3 (rR 2 ) − I, as well as Eqs. (19), (26), and (31). The roots of the Fibonacci spectral polynomial p 21 (E) determine the fifth order fragmentation pattern of the energy spectrum.…”

Section: Third Fourth and Fifth Order Fragmentation Patternsmentioning

confidence: 99%

“…Previous studies have demonstrated that several characteristic physical properties of one-dimensional quasiperiodic lattices, like the fractal structure of their energy spectra and their related eigenstates, can be understood in terms of resonance effects involving a relatively small number of atomic clusters of progressively increasing size. In most of these works, this scenario has been discussed in terms of real-space based renormalization group approaches considering either the mathematically simpler, but chemically unrealistic, diagonal (different types of atoms connected by the same type of bond) and off-diagonal (the same type of atom but different types of bonds between them) models [12][13][14][15][16][17][18][19]. Relatively fewer works have been addressed to the mathematically more complex general case in which both 1700078 (2 of 12) E. Maciá: Clustering resonance effects in electronic energy spectrum diagonal and off-diagonal terms are present in the model Hamiltonian [20][21][22][23][24][25][26][27].…”

mentioning

confidence: 99%

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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Renormalization approach to the electronic localization and transport in macroscopic generalized Fibonacci lattices

Cited by 15 publications

References 29 publications

Lempel-Ziv Complexity of Photonic Quasicrystals

Lempel-Ziv Complexity of Photonic Quasicrystals

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

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

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