Abstract : This thesis in physics constitutes a theoretical study of the edge states in bi-dimensional crystals which exhibit two Dirac cones (spin degenerated) in their dispersion relation. The two systems considered are both the graphene and the square lattice with half a magnetic quantum flux per plaquette. The analytical description of the dispersive energy levels in a high magnetic field (quantum Hall effect regime) due to the presence of edges is highlighted. According to the geometry of the crystal lattice and the shape of the edge, different kinds of coupling are induced between the components of the wave function. This gives rise to various structures of edge sates which however can be described in a common way. Without any magnetic field, some edge states can also exist in these systems, but they have a different origin and their existence itself depends on the shape of the edge. In the case of graphene, we show how to connect the existence of these edge states with a particular type of Berry phase, the so-called Zak phase. This approach allows, for instance, to understand how to manipulate these edge states by tuning the bulk parameters, what involves a topological transition of the Zak phase. Another type of topological transition has also been studied. It consists in the merging of the Dirac cones in the square lattice with half a quantum flux. We show that the mechanism leading to such a phenomena strongly differs from the one known in graphene, and that the physics around the transition can however be described within the same effective Hamiltonian. A shorter second part deals with the weak localization on a disordered cylinder with electronic interactions. The aim of this study is to illustrate the role of the geometry in the decoherence mechanisms due to electron-electron interactions in diffusive systems. The harmonics of the weak localization correction calculated reveal different regimes which probe the different length scales characterizing the decoherence. These lengths underline the sensibility of coherent processes to the geometry and are characterized by specified power laws in temperature.
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Contributor : Pierre Delplace <>
Submitted on : Monday, July 11, 2011 - 11:40:22 AM
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  • HAL Id : tel-00607781, version 1



Pierre Delplace. ÉTATS DE BORD ET CÔNES DE DIRAC DANS DES CRISTAUX BIDIMENSIONNELS. Matière Condensée [cond-mat]. Université Paris Sud - Paris XI, 2010. Français. ⟨tel-00607781⟩



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