Electronic stability of disordered systems: application to quasicrystals
Résumé
The author studies energetic stability of disordered binary alloys in which atoms are interacting via a tight-binding Hamiltonian. In 1D, for a weak potential, the gain in energy compared to the periodic linear chain is derived as a function of the electronic filling factor and the disorder. Very precise results are given in the case of a quasiperiodic arrangement. This kind of phase plays a very particular role since it is shown that for a given filling factor v (or Fermi level position), the most stable structure is a quasiperiodic one associated to v. Moreover, for this structure the fluctuations of the density are unbounded if v and the stoichiometric coefficients do not fulfil an arithmetical condition. Different features are observed for rational and irrational values of v.