Application of renormalization and convolution methods to the Kubo-Greenwood formula in multidimensional Fibonacci systems

Sánchez, Vicenta; Wang, Chumín

doi:10.1103/physrevb.70.144207

Cited by 35 publications

(34 citation statements)

References 21 publications

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“…For instance, the decagonal quasicrystals can be visualized as a periodic stacking of quasiperiodic layers and their Hamiltonian can be expressed as a sum of the periodic and quasiperiodic parts within the first-neighbour tight-binding approximation. Combining the renormalization and convolution methods, the electrical conductivity can be expressed as [12] ð, !, T Þ ¼ 1 ? Electronic transport in multidimensional Fibonacci lattices or ð, !, T Þ ¼ 1 ?…”

Section: The Methods Of Renormalization Plus Convolutionmentioning

confidence: 99%

Electronic transport in multidimensional Fibonacci lattices

Sánchez¹,

Wang²

2006

Philosophical Magazine

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In this article, the Kubo-Greenwood formula is used to investigate the electronic transport behaviour in macroscopic systems by means of an exact renormalization method. The convolution technique is employed in the analysis of two-dimensional Fibonacci lattices. The dc electrical conductance spectra of multidimensional systems exhibit a quantized behaviour when the electric field is applied along a periodically arranged atomic direction, and it becomes a devil's stair if the perpendicular subspace of the system is quasiperiodic. The spectrally averaged conductance shows a power-law decay as the system length grows, neither constant as in periodic systems nor exponential decays occurred in randomly disordered lattices, revealing the critical localization nature of the eigenstates in quasicrystals. Finally, the ac conductance along periodic and quasiperiodic directions is compared with the optical conductivity measured in decagonal quasicrystals.

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Section: The Methods Of Renormalization Plus Convolutionmentioning

confidence: 99%

Electronic transport in multidimensional Fibonacci lattices

Sánchez¹,

Wang²

2006

Philosophical Magazine

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“…To further analyze this important issue the study of the ac conductivity at zero temperature is very convenient, since it is very sensitive to the distribution nature of eigenvalues and the localization properties of the wave function close to the Fermi energy. In this way, by comparing the ac conductivities corresponding to both periodic and general Fibonacci lattices it was concluded that the value of the ac conductivity takes on systematically smaller values in the Fibonacci case, due to the fact that the ac conductivity involves the contribution of nontransparent states within an interval of ℎ around the Fermi level in this case [90,91].…”

Section: Transparent Extended 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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“…This occurs because the number of atoms of the FD is much less than the number of atoms of the PC. Moreover, since the number of atoms of the FD is even, its inclusion destroys the unique state with transmission coefficient equal to one (E ¼ 0) [15] for any value of t FP or t FF .…”

mentioning

confidence: 98%

“…In order to determine the electrical conductivity, in this paper we use the Kubo-Greenwood formula (2) including a renormalization technique described in Ref. [15]. All our systems are connected to two semiinfinite periodic leads with null self-energies and hopping integrals t and the principal chain (PC), shown as blue elements in Fig.…”

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confidence: 99%

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Kubo conductivity of macroscopic systems with Fano defects for periodic and quasiperiodic cases by means of renormalization methods in real space

García

Sánchez

2013

Phys. Status Solidi A

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In this paper, we investigate the effects on the electrical conductivity originated by the inclusion of Fano defects (FDs) for periodic and quasiperiodic systems of macroscopic size. This study is developed using the extension of the methods of renormalization for the Kubo-Greenwood formula in real space within the tight-binding formalism. Within this formalism, the conductivity is determined in an exact form, without any other approximation. For periodic systems, we find the zeros of conductivity located at the eigenenergies of the coupled chain of N F atoms, and transparent states at the eigenenergies of a chain of N F À 1 atoms. These results are shown in both numerical and analytical way. Moreover, the position of the FD in the system does not alter the conductivity spectrum. On the other hand, for quasiperiodic systems, only some coupled chains preserve the transparent state; this was found both numerically and analytically. The case of two FDs attached to the system is also analyzed, founding a high dependence of the electrical conductivity on the distance between the FDs. Finally, this study is extended to two dimensions.

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Application of renormalization and convolution methods to the Kubo-Greenwood formula in multidimensional Fibonacci systems

Cited by 35 publications

References 21 publications

Electronic transport in multidimensional Fibonacci lattices

Electronic transport in multidimensional Fibonacci lattices

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

Kubo conductivity of macroscopic systems with Fano defects for periodic and quasiperiodic cases by means of renormalization methods in real space

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