Energy level statistics of electrons in a 2D quasicrystal

Details Energy level statistics of electrons in a 2D quasicrystal Energy level statistics of electrons in a 2D quasicrystal

1994-01-19

arxiv.org/abs/cond-mat/9401038v1

Physics

Condensed Matter

9 pages including references and figure captions, 6 figures available upon request, LATEX, report-number els1

Scientific paper

10.1103/PhysRevB.51.179

A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics for the randomized tilings follow the predictions of random matrix theory, while for the perfect tilings a new type of level statistics is found. In this case, the first-, second- level spacing distributions are well described by lognormal laws with power law tails for large spacing. In addition, level spacing properties being related to properties of the density of states, the latter quantity is studied and the multifractal character of the spectral measure is exhibited.

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