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Spectral Properties of a Chain of Polyhedra
Author(s) -
Lazo E.
Publication year - 1992
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221690210
Subject(s) - polyhedron , hamiltonian (control theory) , vertex (graph theory) , physics , transverse plane , chain (unit) , formalism (music) , electronic structure , inversion (geology) , combinatorics , topology (electrical circuits) , pure mathematics , condensed matter physics , mathematics , quantum mechanics , engineering , biology , art , mathematical optimization , graph , musical , paleontology , structural engineering , structural basin , visual arts
The electronic structure of a generalized linear chain formed by polyhedra joined at their vertices is studied. Our model incorporates distinct longitudinal and transverse hoppings with respect to the chain axis, producing a variety of paths between consecutive vertex atoms in the backbone chain. The problem is formulated in terms of the Green function formalism, using a tight‐binding Hamiltonian. The infinite set of equations is solved by means of the matrix inversion method. The changes produced in the electronic structure under the topological changes in the connectivity of vertex atoms is investigated when the number of basal atoms is varied. Two continuous bands, separated by a gap are obtained, even when all hoppings are the same. As a particular case of our model the local density of states of the usual linear chain is obtained.