Spectrum of 1D quasicrystals near the periodic chain

Clément Sire (1) , Rémy Mosseri

1 LPS - Laboratoire de Physique des Solides

A tight binding model on the general 1D quasiperiodic chain is studied in the framework of perturbation theory, near the corresponding periodic chain, using a new set of coordinates. The main gaps are well described, whereas the very small ones are correctly given, only for a very small perturbation. For a given irrational number, the energies where the gaps appear in the periodic chain spectrum, are exactly derived.

Mots clés: Theoretical study; Tight binding approximation; One dimensional model; Density of states; Energy gap; Hamiltonian; Band structure; Perturbation theory; Periodic system; Fibonacci sequence

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

Clément Sire, Rémy Mosseri. Spectrum of 1D quasicrystals near the periodic chain. Journal de Physique, 1990, 50, pp.3447. ⟨10.1051/jphys:0198900500240344700⟩. ⟨hal-00123764⟩