Physics – Condensed Matter
Scientific paper
1995-06-02
Physics
Condensed Matter
18 pages special macros jnl.tex,reforder.tex, eqnorder.tex
Scientific paper
10.1088/0953-8984/7/47/009
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an infinite approximant network in analytical form; b) to determine, also analytically, the quantum resistance of a finite strip of a network under appropriate boundary conditions. As a result of a subtle interplay between topology and phase interferences, we find that a strip of phason-defects along a special symmetry direction of a low 2-d Penrose approximant, leads to the rigorous vanishing of the reflection coefficient for certain energies. A similar behavior appears in a low 3-d approximant. This type of ``resonance" is discussed in connection with the gap structure of the corresponding ordered (undefected) system.
Moulopoulos Konstantinos
Roche Stephan
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