ELECTRONIC SPECTRUM OF THE THREE-DIMENSIONAL PENROSE LATTICE
Vekilov Yu.Kh., Isaev E.I., Godoniuk A.V.

Received: March 18, 2003

PACS: 71.23.Ft, 71.30.+h

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Electronic spectrum of the three-dimensional Penrose lattice with «central» decoration by atoms is investigated using the tight binding model with the nearest-neighbor interaction. Inverse participation ratios, higher moments of density probabilities, and fractal dimensions of the system are determined. The wave functions are critical (have a power-law dependence on the distance) at all energies in the band and are multifractal measures leading to the entire spectrum of the exponents. The results show that the system is in the critical state of the metal-insulator transition. On critical wave functions, the cubic root temperature dependence of the conductivity is obtained.