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Etude de jonctions entre canaux de bord de l'effet Hall quantique fractionnaire

Abstract : In this thesis, we deal with interactions between edge states in
Fractional quantum Hall effect. Our work is grounded on recent
experimental realizations of structures -quantum line junctions- in
which this effect is enhanced.

We first introduce the quantum Hall effect emphasizing the edge
states description.

Then, we calculate the tunnel current trough such a junction by
considering the Luttinger liquid theory. We discuss various regimes
of current by varying the junction length, the strength of the
interactions, the filling factor and the temperature.We also
calculate the associated noise.

In a third part, we extend this study to a corner junction, where
edge channels can be either counter-propagating or co-propagating.
In the counter-propagating case, there is a
commensurable-incommensurable phase transition as a function of the
strength of the interactions and of an additionnal parameter: the
incommensurability. In the co-propagating case, we calculate the
tunnel current perturbatively, from a chiral sine-Gordon model.

Eventually, we obtain the density profiles and the elementary
excitations of the system. We evidence an instability in the
dispersion relation of these junctions when the inter-edge
interaction is strong enough. The mean field Chern-Simons theory
predicts an edge reconstruction by the interactions.
Complete list of metadatas
Contributor : Nicolas Regnault <>
Submitted on : Tuesday, February 7, 2006 - 2:11:18 PM
Last modification on : Thursday, December 10, 2020 - 12:36:53 PM
Long-term archiving on: : Saturday, April 3, 2010 - 7:45:44 PM



  • HAL Id : tel-00011553, version 1


Manuel Aranzana. Etude de jonctions entre canaux de bord de l'effet Hall quantique fractionnaire. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00011553⟩



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