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The electronic structure of radially polarized excitons in structured nanorings is analyzed, with emphasis in the ground-state properties and their dependence under applied magnetic fields perpendicular to the ring plane. The electron-hole Coulomb attraction has been treated rigorously, through numerical diagonalization of the full exciton Hamiltonian in the non-interacting electron-hole pairs basis. Depending on the relative weight of the kinetic energy and Coulomb contributions, the ground-state of polarized excitons has "extended" or "localized" features. In the first case, corresponding to small rings dominated by the kinetic energy, the ground-state shows Aharonov-Bohm (AB) oscillations due to the individual orbits of the building particles of the exciton. In the localized regime, corresponding to large rings dominated by the Coulomb interaction, the only remaining AB oscillations are due to the magnetic flux trapped between the electron and hole orbits. This dependence of the exciton, a neutral excitation, on the flux difference confirms this feature as a signature of Coulomb dominated polarized excitons. Analytical approximations are provided in both regimens, which accurate reproduce the numerical results., Comment: 9 pages, including 6 figures

Application de cette approche dans tout le domaine de remplissage. La transformation repulsion-attraction de l'hamiltonien s'avere valable egalement pour cette approximation particuliere du champ moyen. On etudie la signification physique de ce resultat

We present a systematic analysis of the fractional-quantum-Hall-effect (FQHE) Hamiltonian in the symmetric gauge and of the Laughlin wave function (LWF). As in the Landau Gauge, it turns out that the ground state (g.s.) is dominated by a multiple-drop parent state composed of drops of constant actual size (the number of electrons in a given drop thus depends on the distance between adjacent Landau orbitals). These drops are further diffused by correlation effects in order to obtain the g.s. We check the accuracy of the LWF to describe this behavior for one-drop parent states (i.e., the situation for less than six particles) but we find that it overestimates correlation effects when more electrons are present. We correct some of the failures of the LWF but others are hard to eradicate without drastic changes, and so we propose a new approximant for the FQHE g.s. Our proposal allows an easy comprehension of the ground state of unpolarized FQHE systems, the ground-state crystallization effect, and the excitation characteristics.

Etude systematique, analytique et numerique, de l'hamiltonien d'effet Hall (incluant le champ electrique Hall) en fonction de la distance entre orbitales de Landau voisines. On trouve une serie d'etats de symetrie elevee, constitues d'un arrangement periodique de gouttes electroniques, qui agissent comme generateurs de l'etat fondamental. On trouve egalement une serie de transitions de phases dans lesquelles la taille de la goutte electronique croit avec la diminution de la distance entre orbitales adjacentes. La difference entre les facteurs de remplissage pairs et impairs devient apparente

The percolation properties and upper critical field of a disordered superconductive square network are calculated by use of the de Gennes-Alexander theory. It is suggested that photolithographic techniques be used to build such artificially disordered systems. The critical exponent of the upper critical field is calculated and found to be $k=0.93\ifmmode\pm\else\textpm\fi{}0.06$ on the metallic side of the percolative transition.