Fractal Nature of the Electronic Structure of a Penrose Tiling Lattice in a Magnetic Field

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概要

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• The one-electron energy spectrum of a Penrose tiling lattice in a magnetic field isstudied with a tight-binding Hamiltonian. We show the following remarkable resultscharacteristic of a Penrose lattice. (l) The density of states in a magnetic field has acentral peak with zero width at zero energy. It is shown that the zero-energy states cor-respond to the ring states in which wavefunction has nonvanishing amplitudes only atthe sites circling the origin. (2) The magnetic field dependence of the energy spectrumshows a butterfly shape caused by Landau quantization. (3) The magnetic fielddependence of the energy spectrum also shows a fractal nature. In particular it ischaracterized by two periods whose ratio is equal to the golden mean (1 -F- ! 5 ) /2, andtwo periods comprising a Fibonacci sequence. We have clarified the origin of this frac-tal behavior of the energy spectrum analytically.

• 社団法人日本物理学会の論文
• 1989-01-15

著者

• Kamimura Hiroshi

  Department Of Applied Physics . Faculty Of Science Tokyo University Of Science

• HATAKEYAMA Tetsuo

  Department of Physics,Faculty of Science,University of Tokyo

• Hatakeyama Tetsuo

  Department Of Physics Faculty Of Science University Of Tokyo

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