Composite Fermion Approach to the Quantum Hall Hierarchy: When it Works and Why

The mean field composite Fermion (MFCF) picture has been qualitatively successful when applied to electrons (or holes) in the lowest Landau level. Because the energy scales associated with Coulomb interactions and with Chern-Simons gauge field interactions are different, there is no rigorous justification of the qualitative success of the MFCF picture. Here we show that what the MFCF picture does is to select from all the allowed angular momentum (L) multiplets of N electrons on a sphere, a subset with smaller values of L. For this subset, the coefficients of fractional parentage for pair states with small relative angular momentum $R$ (and therefore large repulsion) either vanish or they are small. This set of states forms the lowest energy sector of the spectrum.Comment: RevTeX + 3 EPS figures formatted into the text with epsf.sty to appear in Solid State Communication

Excitations of the ν=5/2\nu=5/2 Fractional Quantum Hall State and the Generalized Composite Fermion Picture

We present a generalization of the composite Fermion picture for a muticomponent quantum Hall plasma which contains particle with different effective charges. The model predicts very well the low-lying states of a $\nu=5/2$ quantum Hall state found in numerical diagonalization.Comment: 5 pages, 3 figure

Charged Excitons in a Dilute 2D Electron Gas in a High Magnetic Field

A theory of charged excitons X- in a dilute 2D electron gas in a high magnetic field is presented. In contrast to previous calculations, three bound X- states (one singlet and two triplets) are found in a narrow and symmetric GaAs quantum well. The singlet and a "bright" triplet are the two optically active states observed in experiments. The bright triplet has the binding energy of about 1 meV, smaller than the singlet and a "dark" triplet. The interaction of bound X-'s with a dilute 2D electron gas is investigated using exact diagonalization techniques. It is found that the short-range character of the e:X- interactions effectively isolates bound X- states from a dilute e-h plasma. This results in the insensitivity of the photoluminescence spectrum to the filling factor nu, and an exponential decrease of the oscillator strength of the dark triplet X- as a function of 1/nu$.Comment: 8 pages, 5 figures, submitted to Phys.Rev.