Electronic properties of a Cantor lattice

Sengupta, Sheelan; Chakrabarti, Abhijit; Chattopadhyay, S.

doi:10.1016/j.physb.2003.09.273

Cited by 11 publications

(11 citation statements)

References 43 publications

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“…The method is well known [22,23], and we do not repeat it to save space. In the example discussed above, the amplitude profile reflects a perfectly extended character, and assumes an interesting lattice-like distribution [16] for a specific value of L A = 0.5. In Fig.4 we show such a lattice-like profile of an extended eigenstate.…”

Section: Transmission Coefficient and The Resonant Eigenstatesmentioning

confidence: 99%

Electronic transport in a Cantor stub waveguide network

2005

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We investigate theoretically, the character of electronic eigenstates and transmission properties of a one dimensional array of stubs with Cantor geometry. Within the framework of real space re-normalization group (RSRG) and transfer matrix methods we analyze the resonant transmission and extended wave-functions in a Cantor array of stubs, which lack translational order. Apart from resonant states with high transmittance we unravel a whole family of wave-functions supported by such an array clamped between two-infinite ordered leads, which have an extended character in the RSRG scheme, but, for such states the transmission coefficient across the lead-sample-lead structure decays following a power-law as the system grows in size. This feature is explained from renormalization group ideas and may lead to the possibility of trapping of electronic, optical or acoustic waves in such hierarchical geometries

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Section: Transmission Coefficient and The Resonant Eigenstatesmentioning

confidence: 99%

Electronic transport in a Cantor stub waveguide network

2005

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“…In Figure 17(a) we plot the wave function amplitudes for one of the solutions of (43) the wave function distribution amplitudes of this state for lattices of different lengths, it was reported that the latticelike feature recurrently appears and disappears depending on the generation order of the fractal lattice, being present for those lattices whose length is given by the series = 3 2 +1 , with ≥ 1 [60]. For other energy values one obtains extended states which, however, do not generally exhibit the lattice-like property as it is shown in Figure 17(b).…”

Section: Eigenstates In On-site Fractal Latticesmentioning

confidence: 98%

“…Thus, both numerical and analytical evidences of localized, critical, and extended wave functions alternating in a complicated way have been reported for several fractal models [54][55][56][57][58][59][60][61][62]. In addition, it was reported that the interplay between the local symmetry and the self-similar nature of a fractal gives rise to the existence of persistent superlocalized modes in the frequency spectrum [63].…”

Section: Fractal Latticesmentioning

confidence: 98%

“…By inspecting these strings we realize that these sequences differ from the binary QP sequences considered in Section 2.2 in the sense that, as the system grows on, the subclusters of s grow in size to span the entire 1D space. Therefore, in the thermodynamic limit the lattice may be looked upon as an infinite string of atoms, punctuated by atoms which play the role of impurities located at specific sites determined by the Cantor sequence [60,65].…”

Section: Fractal Latticesmentioning

confidence: 99%

“…Accordingly, when −1 is a multiple of 3 the state becomes transparent, elsewhere one gets (0) = 4/5 = 0.8, as it is the case of the eigenstate shown in Figure 17 for a lattice with = 3 5 sites. Therefore, among the extended wave functions belonging to the triadic Cantor lattice spectrum energy one can find both transparent and nontransparent states, depending upon the adopted value [60].…”

Section: Transparent Extended States In Aperiodic Systemsmentioning

confidence: 99%

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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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Local symmetry dynamics in one-dimensional aperiodic lattices: a numerical study

et al. 2014

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A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry possess characteristic distributional and dynamical properties which can be determined for every aperiodic binary lattice. A striking aspect of such a property is given by the return maps of sequential spacings of local symmetry axes, which typically traverse few-point symmetry orbits. This local symmetry dynamics allows for a classification of inherently different aperiodic lattices according to fundamental symmetry principles. Illustrating the local symmetry distributional and dynamical properties for several representative binary lattices, we further show that the renormalized axis spacing sequences follow precisely the particular type of underlying aperiodic order. Our analysis thus reveals that the long-range order of aperiodic lattices is characterized in a compellingly simple way by its local symmetry dynamics.

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Electronic properties of a Cantor lattice

Cited by 11 publications

References 43 publications

Electronic transport in a Cantor stub waveguide network

Electronic transport in a Cantor stub waveguide network

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

Local symmetry dynamics in one-dimensional aperiodic lattices: a numerical study

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