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Formation d'une molécule de Wigner sur un réseau bidimensionnel : structure et aimantation

Abstract : The phase diagram of a quantum system of electrons, with both Coulombian interactions and disorder, is numerically investigated in this work. From the exact diagonalization of a lattice model, using Lanczos techniques, we obtain the eigen-values and vectors of the system. These studies are motivated by recent experiments (1994 Kravchenko et al), which show a metal-insulator transition in two-dimensional gases, when the Coulombian energy is around ten times the Kinetic one. We develop the perturbative expansion around the Wigner crystal. Particularly, we have calculated the persistent current, whose sign, which is disorder independent, is given here by a simple rule. We have also studied few-electron systems, where we emphasis a link between the behaviour of those systems and the experimental results on transport and magnetism (1999 Mertes et al). Particularly, we show the existence of a regime, at intermediate interactions, between the Wigner crystal at strong interactions and the Fermi glass at weak interactions. In this intermediate regime, the ground state possesses some properties of both solid and liquid states, which is in agreement with the conjecture of Andreev-Lifshitz. In the last part, we tackle the problem of two-interacting particles on a disordered chain, where a local interaction leads to a delocalization of a few states (1994 Shepelyansky). With a Coulombian interaction, we show that we have a spatial delocalization for these states. We also see that the spectral statistics are the same as the statistics of diffusive metal: We reach the Wigner-Dyson statistics whereas the local interaction leads only to semi-Poisson statistics.
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https://tel.archives-ouvertes.fr/tel-00001528
Contributor : Marc Gingold <>
Submitted on : Thursday, August 1, 2002 - 8:46:51 AM
Last modification on : Friday, March 5, 2021 - 3:00:45 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 5:40:50 PM

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  • HAL Id : tel-00001528, version 1

Citation

Franck Selva. Formation d'une molécule de Wigner sur un réseau bidimensionnel : structure et aimantation. Matière Condensée [cond-mat]. Université Pierre et Marie Curie - Paris VI, 2002. Français. ⟨tel-00001528⟩

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