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Register a new userComposite Fermion Geometric Resonance Near { u} = 1/2 Fractional Quantum Hall State
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We observe geometric resonance features of composite fermions on the flanks of the even denominator { u} = 1/2 fractional quantum Hall state in high-mobility two-dimensional electron and hole systems confined to wide GaAs quantum wells and subjected to a weak, strain-induced, unidirectional periodic potential modulation. The features provide a measure of how close to { u} = 1/2 the system stays single-component and supports a composite fermion Fermi sea before transitioning into a { u} = 1/2 fractional quantum Hall state, presumably the two-component {Psi}331 state.
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Via the application of parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells, and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors $ u=1$ and 1/2. Near $ u=1$, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to $ u=1/2$, CFs appear single-layer-like (single-component) as their resonance features correspond to the total density.
A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption the phonon exchange attraction between the conduction electron (electron, hole) and fluxons (quanta of magnetic fluxes). We postulate that c-fermions with emph{any} even number of fluxons have an effective charge (magnitude) equal to the electron charge $e$. The density of c-fermions with $m$ fluxons, $n_phi^{(m)}$, is connected with the electron density $n_{mathrm e}$ by $n_phi^{(m)}=n_{mathrm e}/m$, which implies a more difficult formation for higher $m$, generating correct values $me^2/h$ for the Hall conductivity $sigma_{mathrm H}equiv j/E_{mathrm H}$. For condensed c-bosons the density of c-bosons-with-$m$ fluxons, $n_phi^{(m)}$, is connected with the boson density $n_0$ by $n_phi^{(m)}=n_0/m$. This yields $sigma_{mathrm H}=m,e^2/h$ for the magnetoconductivity, the value observed of the QHE at filling factor $ u=1/m$ ($m=$odd numbers). Laughlins theory and results about the fractional charge are not borrowed in the present work.
We report quantitative measurements of the impact of alloy disorder on the $ u=5/2$ fractional quantum Hall state. Alloy disorder is controlled by the aluminum content $x$ in the Al$_x$Ga$_{1-x}$As channel of a quantum well. We find that the $ u=5/2$ state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the $ u=5/2$ state appears at significantly reduced mobilities when compared to samples in which alloy disorder is not the dominant scattering mechanism. Our results highlight the distinct roles of the different types of disorder present in these samples, such as the short-range alloy and the long-range Coulomb disorder.
In bilayer quantum Hall systems at filling fractions near nu=1/2+1/2, as the spacing d between the layers is continuously decreased, intra-layer correlations must be replaced by inter-layer correlations, and the composite fermion (CF) Fermi seas at large d must eventually be replaced by a composite boson (CB) condensate or 111 state at small d. We propose a scenario where CBs and CFs coexist in two interpenetrating fluids in the transition. Trial wavefunctions describing these mixed CB-CF states compare very favorably with exact diagonalization results. A Chern-Simons transport theory is constructed that is compatible with experiment.
We observe fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor $ u=1/2$ in two-dimensional hole systems confined to GaAs quantum wells of width 30 to 50 nm and having bilayer-like charge distributions. The $ u=1/2$ FQHE is stable when the charge distribution is symmetric and only in a range of intermediate densities, qualitatively similar to what is seen in two-dimensional electron systems confined to approximately twice wider GaAs quantum wells. Despite the complexity of the hole Landau level structure, originating from the coexistence and mixing of the heavy- and light-hole states, we find the hole $ u=1/2$ FQHE to be consistent with a two-component, Halperin-Laughlin ($Psi_{331}$) state.
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