Theoretical Study of phases with inhomgeneous density in quantum Hall systems
Etude theorique des phases de densite inhomogene dans les systemes a effet Hall quantique
Résumé
The issue of this thesis is the study of the different electron-solid and quantum-liquid phases, which are found in two-dimensional electron systems under a perpendicular magnetic field. The formation of these phases is due to the strong Coulomb repulsion between the electrons of a partially filled Landau level. The energy calculations of the thesis allow one to understand recent experimental investigations, which have revealed a non-monotonic behaviour of the transverse (Hall) resistance. This effect is due to multiple first-order transitions between the competing phases. The derivation of a model of interacting composite fermions - the quasiparticles responsible for the fractional quantum Hall effect - furthermore allows for the study of new phases, which occur at high magnetic fields. Most saliently, a recently observed fractional quantum Hall effect at unusual values of the field has been identified as the manifestation of a second generation of composite fermions.
L'objet de cette these est l'etude des differentes phases solides electroniques et liquides quantiques, que l'on trouve dans des systemes electroniques bi-dimensionnels exposes a un champ magnetique perpendiculaire. La formation de ces phases est due aà la repulsion coulombienne entre les electrons restreints a un niveau de Landau partiellement rempli. Les calculs d'energie de cette these permettent de comprendre des etudes experimentales recentes, qui ont mis en evidence un comportement non monotone de la resistance transverse (de Hall). Cet effet est du a des transitions multiples de premier ordre entre les phases en competition. La deduction d'un modele de fermions composites en interaction - les quasi-particules responsables de l'effet Hall quantique fractionnaire - permet de plus l'etude de nouvelles phases qui paraissent a fort champ magnetique. En particulier, un effet Hall quantique fractionnaire a des valeurs inhabituelles du champ a ete identifie comme la manifestation d'une deuxieme generation de fermions composites.