Singular localised states in quasiperiodic GaAs/Al_xGa_{1 − x} As Fibonacci superlattices

Faculté des sciences et sciences de l'ingénieur, Université de Mostaganem, BP 188, 27000 Mostaganem, Algeria

Corresponding author: aziz_zdz@yahoo.fr

Received: 26 March 2006
Accepted: 24 May 2006
Published online: 19 July 2006

Abstract

We examine numerically the effect of quasiperiodicity in the nature of the states in Fibonacci semiconductor superlattices by means of the transfer matrix formalism. We are interested in the GaAs/Al_xGa_{1 − x} As layers, having identical thickness, where the aluminium concentration x takes, two different values. We have found that each miniband of the periodic superlattice splits in several sub-minibands, that is small minigaps appear. We demonstrate that the origin of these small inner minigaps is due to the loss of long-range quantum coherent of the electrons wave. The corresponding electronic spectrum shows a high fragment. The states having transmission coefficient close to zero in the minibands can be viewed as consisting of singular localised states.