Renormalization and envelope function formalism for incommensurate systems |
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Authors: | R Farchioni G Grosso G Pastori Parravicini |
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Institution: | 1. Dipartimento di Fisica dell'Università Consorzio Interuniversitario Nazionale Fisica della Materia, Gruppo Nazionale Struttura della Materia, piazza Torricelli 2, 56126, Pisa, Italia 2. Dipartimento di Fisica ?A. Volta? dell'Università Consorzio Interuniversitario Nazionale Fisica della Materia, Gruppo Nazionale Struttura della Materia, via Bassi 6, 27100, Pavia, Italia
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Abstract: | 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.
In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching. |
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Keywords: | Localized single-particle electronic states (excluding impurities) |
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