Electronic stability of quasicrystals: application to flux phases

Abstract

The energetic stability of disordered binary alloys in which electrons are interacting via a tight-binding Hamiltonian is considered. A phenomenological repulsive interatomic potential is also added to the Hamiltonian. For a weak potential, the gain in energy compared to the periodic linear chain is derived as a function of the electronic filling factor ν, and the disorder. For a given ν, the most stable structure is a quasiperiodic chain associated with ν and the atomic concentration. These results, which are exact for any concentration and filling factor, are illustrated on the quasiperiodic Fibonacci chain. As an application, we show that the preceding results favor the stability of uniform flux phases with a flux per plaquette Φ = ν.