Excitation spectrum, extended states, gap closing : some exact results for codimension one quasicrystals
Résumé
In this paper, we study a tight-binding Hamiltonian for codimension one quasicrystals by means of a new numbering which orders the sites according to their environment. This includes the general 1D quasiperiodic chain. We exhibit exact extended wave functions on approximants for the general quasiperiodic chain, for which we define a « quasi-Bloch » vector. These extended states can be shown to be degenerate. Moreoever, some of them correspond to energies where gaps disappear, when the tight-binding parameters vary. We also exhibit a surface of the three dimensional space of parameters, which intersects the spectrum of all 1D quasiperiodic chains which can be generated by the standard cut and projection algorithm from 2D. The consequences of these properties on physical quantities such as the conductivity are briefly discussed. These results, although being general, are illustrated on the Fibonacci chain.
Domaines
Articles anciens
Origine : Accord explicite pour ce dépôt
Loading...