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Phase de bi-particules localisées par interaction attractive dans un milieu aléatoire

Abstract : We study the effects of the interplay between interaction and disorder on the localization of fermionic particles. We show that the setting up, above the Fermi level, of an attractive Hubbard interaction between two particles living on a (two- or three dimensional) disordered Anderson lattice leads, in the ground state, to the creation of a pair of localized particles. This biparticle phase appears in a regime of disorder where the noninteracting particles are not yet localized (metallic phase of the Anderson model). This localization persists also for excited states describing a state of two bounded particles. This phase of localized biparticles induced by the attractive interaction (BLS phase) is however superseded by a phase of delocalized Cooper pairs when the fluctuations of the disorder on the lattice become sufficiently weak. A magnetic field can affect the pair structure of the localized states leading to the delocalization of the particles and then to the disappearance of the BLS phase. For disordered systems, this two-particle model is a generalization of the Cooper's Problem. We show then that it is necessary to go beyond the usual Cooper's ansatz in order to describe correctly the BLS phase. This result implies, for the many-body case, that the mean-field approximation techniques using the pairing suggested by the Cooper's ansatz do not allow to treat satisfactorily the interplay between disorder and attraction in strongly disordered superconductors. An extension of our model for N>2 interacting fermions is given showing that the N-body ground state undertakes a transition from a delocalized (superconducting) state to a localized (insulating) state when the disorder increases in the system.
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Contributor : José Lages <>
Submitted on : Wednesday, January 12, 2005 - 2:28:58 AM
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  • HAL Id : tel-00008016, version 1


José Lages. Phase de bi-particules localisées par interaction attractive dans un milieu aléatoire. Matière Condensée [cond-mat]. Université Paul Sabatier - Toulouse III, 2001. Français. ⟨tel-00008016⟩



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