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Chasse aux papillons (quantiques) colorés : Une dérivation géométrique des équations TKNN

I consider the Hofstadter and the Harper operators, regarded as e ective models for a Bloch electron in a uniform magnetic eld, in the limit of weak and strong eld respectively. For each value of the Fermi energy in a spectral gap, I prove that the corresponding Fermi projectors exhibit a geometric duality, expressed in terms of some vector bundles canonically associated to the projectors. As a corollary, I get a rigorous geometric derivation of the TKNN equations. More generally, I prove that analogous equations hold true for any orthogonal projector in the rational rotation C -algebra, alias the algebra of the (rational) noncommutative torus.

Identiferoai:union.ndltd.org:CCSD/oai:tel.archives-ouvertes.fr:tel-00674271
Date29 October 2010
CreatorsDe Nittis, Giuseppe
Source SetsCCSD theses-EN-ligne, France
LanguageEnglish
Detected LanguageEnglish
TypePhD thesis

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