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Il Nuovo Cimento D

, Volume 15, Issue 2–3, pp 375–392 | Cite as

Renormalization and envelope function formalism for incommensurate systems

  • R. Farchioni
  • G. Grosso
  • G. Pastori Parravicini
Article
  • 29 Downloads

Summary

We study the localization-delocalization transition in one-dimensional incommensurate crystals both numerically and analytically. From the numerical point of view we provide an implementation of the renormalization method, which allows to process with high accuracy millions of sites (whenever necessary). From the analytic point of view we extend the envelope function concepts to incommensurate potentials, smoothly varying on lattice constant scale. The control of the transition is made by numerical calculation of the Lyapunov exponent: it presents surprising aspects of universality and simplicity, with plateaux, linear regions and, at times, much more complicated behaviours. The envelope function method, together with semi-analytic considerations, allows to understand, in a number of situations, the presence of mobility edges, pseudo-mobility edges, and gaps in the energy spectrum.

PACS 71.50

Localized single-particle electronic states (excluding impurities) 

PACS 71.30

Metal-insulator transitions 

PACS 73.20.Dx

Electron states in low-dimensional structures (including quantum wells, superlattices, layer structures, and intercalation compounds) 

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Copyright information

© Società Italiana di Fisica 1993

Authors and Affiliations

  • R. Farchioni
    • 1
    • 2
  • G. Grosso
    • 1
  • G. Pastori Parravicini
    • 2
  1. 1.Dipartimento di Fisica dell'Università Consorzio Interuniversitario Nazionale Fisica della MateriaGruppo Nazionale Struttura della MateriaPisaItalia
  2. 2.Dipartimento di Fisica «A. Volta» dell'Università Consorzio Interuniversitario Nazionale Fisica della MateriaGruppo Nazionale Struttura della MateriaPaviaItalia

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