Es. Zijlstra et T. Janssen, Localization of electrons and influence of surface states on the density of states in a tight-binding model on the Penrose tiling, MAT SCI E A, 294, 2000, pp. 886-889
The distribution of participation numbers of electronic states in the verte
x model of the Penrose tiling (PT) is calculated for a series of approximan
ts and eight fixed values of the energy by means of contour integrations in
the first Brillouin zone. Localization of electrons is seen to depend on e
nergy. The local density of states at the surface of a small approximant of
the PT is compared to the density of states (DOS) of the same approximant
with periodic boundary conditions. The large difference between the two cur
ves indicates that surface states might be responsible for the fact that ex
perimentally surface sensitive techniques do not resolve spikes in the DOS
of quasicrystals. The DOS of the (8,5) approximant of the three-dimensional
PT is shown to be less spiky than expected. (C) 2000 Elsevier Science B.V.
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