Simple model for a quantum wire II. Statistically correlated disorder

Abstract:

In a previous paper (Eur. Phys. J. B 30, 239-251 (2002)) we have presented the main features and properties of a simple model which -in spite of its simplicity- describes quite accurately the qualitative behaviour of a quantum wire. The model was composed of N distinct deltas each one carrying a different coupling. We were able to diagonalize the Hamiltonian in the periodic case and yield a complete and analytic description of the subsequent band structure. Furthermore the random case was also analyzed and we were able to describe Anderson localization and fractal structure of the conductance. In the present paper we go one step further and show how to introduce correlations among the sites of the wire. The presence of a correlated disorder manifests itself by altering the distribution of states and the localization of the electrons within the system.