Localization of Electronic Wave Functions on Quasiperiodic Lattices

Thomas Rieth; Uwe Grimm; Michael Schreiber

doi:10.1088/0953-8984/10/4/008

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Localization of Electronic Wave Functions on Quasiperiodic Lattices

Thomas Rieth·Uwe Grimm·Michael Schreiber

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Abstract

We study electronic eigenstates on quasiperiodic lattices using a tight-binding Hamiltonian in the vertex model. In particular, the two-dimensional Penrose tiling and the three-dimensional icosahedral Ammann-Kramer tiling are considered. Our main interest concerns the decay form and the self-similarity of the electronic wave functions, which we compute numerically for periodic approximants of the perfect quasiperiodic structure. In order to investigate the suggested power-law localization of states, we calculate their participation numbers and structural entropy. We also perform a multifractal analysis of the eigenstates by standard box-counting methods. Our results indicate a rather different behaviour of the two- and the three-dimensional systems. Whereas the eigenstates on the Penrose tiling typically show power-law localization, this was not observed for the icosahedral tiling.

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Thomas Rieth, Uwe Grimm, Michael Schreiber. 1998-09-07. Localization of Electronic Wave Functions on Quasiperiodic Lattices. https://doi.org/10.1088/0953-8984%2F10%2F4%2F008

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