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Document Type: Artigo
Title: Localization properties of a tight-binding electronic model on the Apollonian network
Authors: Souza, André Maurício Conceição de
Cardoso, Ariston de Lima
Andrade, Roberto Fernandes Silva
Issue Date: Dec-2008
Abstract: An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex network and as a substrate on the top of which physical models can be defined. The Schrödinger equation of the model, which includes only nearest-neighbor interactions, is written in a matrix formulation. In the uniform case, the resulting Hamiltonian is proportional to the adjacency matrix of the Apollonian network. The characterization of the electronic eigenstates is based on the properties of the spectrum, which is characterized by a very large degeneracy. The 2π/3 rotation symmetry of the network and large number of equivalent sites are reflected in all eigenstates, which are classified according to their parity. Extended and localized states are identified by evaluating the participation rate. Results for other two nonuniform models on the Apollonian network are also presented. In one case, interaction is considered to be dependent of the node degree, while in the other one random on-site energies are considered.
Keywords: Transição de Anderson
Apollonian network
ISSN: 1550-235X
Publisher / Institution : American Physical Society
Citation: CARDOSO, A. L.; ANDRADE, R. F. S.; SOUZA, A. M. C. Localization properties of a tight-binding electronic model on the Apollonian network. Physical Review B, New York, v. 78, n. 21, dez. 2008. Disponível em: <>. Acesso em: 18 mar. 2013.
License: Copyrights American Physical Society
Appears in Collections:DFI - Artigos de periódicos

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