Energy spectra and eigenstates of electrons in planar quasicrystals

Uwe Grimm, Applied Maths Department, the Open University

Abstract:

Some analytical and numerical results for quasiperiodic tight-binding

models are summarised, with an emphasis on two-dimensional models

which so far are beyond a mathematically rigorous treatment. In

particular, energy spectra of aperiodic tight-binding models and the

corresponding energy level statistics, which are well reproduced by

random matrix theory, are considered. The eigenstates are characterised

by multifractal analysis, and a construction of peculiar multifractal states

on the Penrose tiling is sketched. Finally, quantum diffusion is discussed

for the toy model of the labyrinth tiling, which allows the numerical

treatment of large systems.