Fractional quantum Hall effect in multicomponent systems

Abstract : We study a number of fractional quantum Hall systems, such as quantum Hall bilayers, wide quantum wells or graphene, where underlying multicomponent degrees of freedom lead to novel physical phenomena. In the quantum Hall bilayer at the filling factor nu=1 we study mixed composite boson-composite fermion trial wave functions in order to describe the disordering of the exciton superfluid as the bilayer distance is increased. We propose wave functions to describe the states of the bilayer for intermediate distances and examine their properties. At the bilayer total filling nu=1/2 and nu=2/5 we study the quantum phase transition between the multicomponent Halperin states and the polarized, Abelian and non-Abelian, phases as the tunneling term is varied. We use a combination of exact diagonalization and the effective BCS model to study the transitions. Furthermore we introduce a realistic model of the wide quantum well which is used to examine even-denominator quantum Hall states at nu=1/2 and nu=1/4 in the lowest Landau level. Finally, we explore some possibilities for the fractional quantum Hall effect in graphene based on the multicomponent picture of spin and valley degrees of freedom.
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Zlatko Papic. Fractional quantum Hall effect in multicomponent systems. Condensed Matter [cond-mat]. Université Paris Sud - Paris XI, 2010. English. ⟨tel-00624760⟩

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