Open AccessTHE ELECTRONIC PROPERTIES OF THE VERTEX MODEL FOR 2-DIMENSION QUASICRYSTALS
Author(s) -
Pingchuan Ma,
Youyan Liu,
Nanzhi Zou,
Yichang Zhou
Publication year - 1990
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.39.100
Subject(s) - degenerate energy levels , hamiltonian (control theory) , eigenvalues and eigenvectors , wave function , quasicrystal , physics , vertex (graph theory) , lattice (music) , quantum mechanics , electronic structure , mathematical physics , condensed matter physics , mathematics , combinatorics , mathematical optimization , graph , acoustics
This paper is devoted to the study on electronic properties of the vertex model of the Penrose lattice with five-fold rotational symmetric axis in the framework of tight-binding Hamiltonian. A similarity transformation is introduced to reduce the Hamiltonian, which helps to determine analytically the degeneracies of the eigenstates and to simplify the numerical calculation for the eigenenergies and the eigenvectors. It is found that two thirds of the states are doubly degenerate and the remains are non-degenerate. This conclusion is confirmed by group theory. The Hoursehold and improved Dean motheds are used to obtain the energy spectra and examine the localication of the electronic states. By several methods and criteria, three kinds of wavefunction behaviors are definitely found. The highly degenerate states are also investgated.