Phys. Rev. B 33, 4936–4940 (1986)Fractal character of wave functions in one-dimensional incommensurate systemsReceived 23 September 1985; published in the issue dated 1 April 1986 The electronic wave functions of simple one-dimensional systems with a modulation potential incommensurate with that of the underlying lattice are determined by a direct diagonalization method. The existence of the metal-insulator transition is also obtained by a renormalization-group method. Numerical evidence for a fractal character of the wave functions is obtained and the fractal dimensionality D is calculated as a function of the strength of the modulation potential V0. At the critical point V0=2t, we find that D=0.80±0.15. The wave functions can also be characterized by the localization length lc and the amplitude correlation length ξ. © 1986 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevB.33.4936
DOI:
10.1103/PhysRevB.33.4936
PACS:
72.10.Bg, 71.55.Jv, 71.50.+t
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