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Localization in random fractal lattices

Arkadiusz Kosior and Krzysztof Sacha
Phys. Rev. B 95, 104206 – Published 27 March 2017

Abstract

We investigate the issue of eigenfunction localization in random fractal lattices embedded in a two-dimensional Euclidean space. In the system of our interest, there is no diagonal disorder—the disorder arises from random connectivity of nonuniformly distributed lattice sites only. By adding or removing links between lattice sites, we change the spectral dimension of a lattice but keep the fractional Hausdorff dimension fixed. From the analysis of energy level statistics obtained via direct diagonalization of finite systems, we observe that eigenfunction localization strongly depends on the spectral dimension. Conversely, we show that the localization properties of the system do not change significantly while we alter the Hausdorff dimension. In addition, for low spectral dimensions, we observe superlocalization resonances and a formation of an energy gap around the center of the spectrum.

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  • Received 23 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.104206

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Arkadiusz Kosior1,2 and Krzysztof Sacha1,3

  • 1Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland
  • 2ICFO-Institut de Ciencies Fotoniques, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels (Barcelona), Spain
  • 3Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland

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Issue

Vol. 95, Iss. 10 — 1 March 2017

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