Extended and critical wave functions in a Thue-Morse chain

Cs, Ryu; Gy, Oh; Mh, Lee

doi:10.1103/physrevb.46.5162

Cited by 90 publications

(62 citation statements)

References 27 publications

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“…2, the second and the fth subbands, respectively, are trifurcate and the others are bifurcate. All these are consistent with the general rule of branching for electronic energy spectra of TM chains, 18,20) which is obtained in the on-site framework under the periodic-boundary conditions. Obviously, the branching rule of the spectra shown here is dierent from that of the Fibonacci superlattice, 17) which is only trifurcate.…”

Section: X3 Frequency Spectrasupporting

confidence: 70%

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Coupled Optical Interface Modes in a Thue–Morse Dielectric Superlattice

et al. 2001

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We study the coupled optical interface modes in a Thue{Morse dielectric superlattice. Based on the electrostatic continuum approximation, which is correct in the long wavelength limit, the transfer matrix method is used to derive the analytic expressions for frequency spectra and electrostatic potential distributions. The numerical calculations show that the frequency spectra are singular continuous, and the potential proles are mostly extended and lattice-like. The common features and pronounced dierences with coupled optical interface modes in periodic and Fibonacci dielectric superlattices as well as with electrons and acoustic phonons in Thue{Morse structures are exposed. Furthermore, the possibility of experimental observation is discussed.

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Section: X3 Frequency Spectrasupporting

confidence: 70%

“…However, the recursion is a little tedious because the initial expressions for 1 and 2 are more complicated than for electrons 7,20) and acoustic phonons. 23) They are…”

Section: X2 the Dielectric Continuum Modelmentioning

confidence: 99%

Coupled Optical Interface Modes in a Thue–Morse Dielectric Superlattice

et al. 2001

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“…It is well known that aperiodic systems possess a dense spectrum of critical modes, featuring unique fractal scaling and spatial localization character with traits intermediate between Anderson and Bloch modes (15,20,21). When these modes are excited, photons can be efficiently trapped on the surface of aperiodic systems enabling enhanced surface interactions in comparison to what can be achieved using traditional optical modes (14).…”

mentioning

confidence: 97%

“…1D) arrays of Cr nanoparticles with minimum center-to-center separation of 300 nm and 400 nm. The spatial complexity of these aperiodic structures is described by the spectral character of their spatial Fourier spectra, which in contrast to simple periodic structures, densely fills the reciprocal space with distinctive fractal properties (19)(20)(21)(22). In particular, Gaussian prime lattices feature nonperiodic Fourier spectra with well defined reciprocal lattice vectors (Bragg-peaks) (19), while the more complex Thue-Morse and Rudin-Shapiro structures display singular continuous and absolutely continuous Fourier spectra (12-15, 17, 18), respectively.…”

mentioning

confidence: 99%

Spatial and spectral detection of protein monolayers with deterministic aperiodic arrays of metal nanoparticles

Lee

Amsden²,

Boriskina

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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Light scattering phenomena in periodic systems have been investigated for decades in optics and photonics. Their classical description relies on Bragg scattering, which gives rise to constructive interference at specific wavelengths along well defined propagation directions, depending on illumination conditions, structural periodicity, and the refractive index of the surrounding medium. In this paper, by engineering multifrequency colorimetric responses in deterministic aperiodic arrays of nanoparticles, we demonstrate significantly enhanced sensitivity to the presence of a single protein monolayer. These structures, which can be readily fabricated by conventional Electron Beam Lithography, sustain highly complex structural resonances that enable a unique optical sensing approach beyond the traditional Bragg scattering with periodic structures. By combining conventional dark-field scattering micro-spectroscopy and simple image correlation analysis, we experimentally demonstrate that deterministic aperiodic surfaces with engineered structural color are capable of detecting, in the visible spectral range, protein layers with thickness of a few tens of Angstroms.biosensing | colorimetric fingerprint | deterministic aperiodic system | nanophotonics

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“…For instance, references to self-similar, chaotic, lattice-like, or quasilocalized wave functions can be found in the literature depending on the different criteria adopted to characterize them [48,[73][74][75]. Generally speaking, critical states exhibit a rather involved oscillatory behavior, displaying strong spatial fluctuations which show distinctive self-similar features ( Figure 5).…”

Section: Nature Of States In Aperiodic Systemsmentioning

confidence: 99%

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

Maciá

2014

ISRN Condensed Matter Physics

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The interest in the precise nature of critical states and their role in the physics of aperiodic systems has witnessed a renewed interest in the last few years. In this work we present a review on the notion of critical wave functions and, in the light of the obtained results, we suggest the convenience of some conceptual revisions in order to properly describe the relationship between the transport properties and the wave functions distribution amplitudes for eigen functions belonging to singular continuous spectra related to both fractal and quasiperiodic distribution of atoms through the space.

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Extended and critical wave functions in a Thue-Morse chain

Cited by 90 publications

References 27 publications

Coupled Optical Interface Modes in a Thue–Morse Dielectric Superlattice

Coupled Optical Interface Modes in a Thue–Morse Dielectric Superlattice

Spatial and spectral detection of protein monolayers with deterministic aperiodic arrays of metal nanoparticles

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

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