Electronic Spectrum of a 2D Quasi-Crystal Related to the Octagonal Quasi-Periodic Tiling

Clément Sire (1)

1 PhyStat - Physique Statistique des Systèmes Complexes (LPT)

Recently, a tiling derived from the well-known 2D quasi-periodic octagonal tiling has been introduced. In this letter, we show that in the framework of a tight-binding model, the electronic spectrum of this nontrivial tiling can be derived. The integrated density of state is singular and can be a devil staircase, there can be a finite or infinite number of gaps, whereas the measure of the spectrum can be zero or not, all these properties depending on the hopping parameters. This transition is explained with a very simple model.

Mots clés: Periodic system; Perturbation theory; Band structure; Quasicrystals; Fibonacci sequence; Fractals; Tight binding approximation; Density of states; Energy gap; Hamiltonian

Domaines: Mécanique statistique [cond-mat.stat-mech]

Clément Sire. Electronic Spectrum of a 2D Quasi-Crystal Related to the Octagonal Quasi-Periodic Tiling. EPL - Europhysics Letters, 1989, 10, pp.483-488. ⟨10.1209/0295-5075/10/5/016⟩. ⟨hal-00472630⟩