The European Physical Journal B - Condensed Matter and Complex Systems

, Volume 30, Issue 2, pp 239–251

Infinite chain of different deltas: A simple model for a quantum wire

  • J.M. Cerveró
  • A. Rodrıguez

DOI: 10.1140/epjb/e2002-00377-4

Cite this article as:
Cerveró, J. & Rodrıguez, A. Eur. Phys. J. B (2002) 30: 239. doi:10.1140/epjb/e2002-00377-4

Abstract:

We present the exact diagonalization of the Schrödinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced.

PACS. 03.65.-w Quantum mechanics – 71.23.An Theories and models; localized states – 73.21.Hb Quantum wires

Copyright information

© EDP Sciences, Springer-Verlag 2002

Authors and Affiliations

  • J.M. Cerveró
    • 1
  • A. Rodrıguez
    • 1
  1. 1.Fısica Teórica, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, SpainES