Energy spectra and photoluminescence of charged magneto-excitons

Charged magneto-excitons X- in a dilute 2D electron gas in narrow and symmetric quantum wells are studied using exact diagonalization techniques. An excited triplet X- state with a binding energy of about 1 meV is found. This state and the singlet are the two optically active states observed in photoluminescence (PL). The interaction of X-'s with electrons is shown to have short range, which effectively isolates bound X- states from a dilute e-h plasma. This results in the insensitivity of PL to the filling factor nu. For the "dark" triplet X- ground state, the oscillator strength decreases exponentially as a function of 1/nu which explains why it is not seen in PL.Comment: 3 pages, 4 figures, submitted to Physica

Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level

We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al. The pseudopotential describing the electron - electron interaction in LL1 is harmonic at short range. It produces a series of incompressible states which is different from its LL0 counterpart. The numerical data indicate that the most prominent states $\nu={5/2}$, 7/3, and 8/3 are not produced by Laughlin correlated electrons, but result from a tendency of electrons to form pairs or larger clusters which eventually become Laughlin correlated. States with smaller gaps at filling factors 14/5, 16/7, 11/5, 19/7 are Laughlin correlated electron or hole states and fit Jain's sequence of filled $\rm{CF}^4$ levels.Comment: 4 pages, 7 figure

Fractionally charged magneto-excitons

The photoluminescence (PL) spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime is studied. The response of the 2DEG to an optically injected valence hole depends on the separation d between the electron and hole layers. At d smaller than the magnetic length lambda, the PL spectrum shows recombination of neutral (X) and charged (X-) excitons. At d>lambda, the hole binds one or two Laughlin quasielectrons (QE) of the 2DEG to form fractionally charged excitons (FCX), hQE or hQE2. Different FCX states have different optical properties, and their stability depends critically on the presence of QE's in the 2DEG. This explains discontinuities observed in the PL spectrum at such (Laughlin) filling factors as nu=1/3 or 2/3.Comment: 4 pages, 4 figures, submitted to PR

Transformation of Statistics in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane's spherical geometry, the Fermion angular momentum l_F is replaced by l_B=l_F-(N-1)/2. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular momentum L_12) increases as L_12(L_12+1). Similar bands of low energy states occur in the two spectra if V increases more quickly than this.Comment: 4 pages, 1 figure, poster at ARW in Queenstown, New Zealand (2001

Search for electron liquids with non-Abelian quasiparticles

We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors $7/3 <\nu_e<8/3$. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at $\nu_e=5/2$ (paired Moore--Read "pfafian" state) and 12/5 (clustered Read--Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline $\nu_e=7/3$ state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.Comment: 9 pages, 8 figure

Three-body correlations and finite-size effects in the Moore--Read states on a sphere

Two- and three-body correlations in partially filled degenerate fermion shells are studied numerically for various interactions between the particles. Three distinct correlation regimes are defined, depending on the short-range behavior of the pair pseudopotential. For pseudopotentials similar to those of electrons in the first excited Landau level, correlations at half-filling have a simple three-body form consisting of the maximum avoidance of the triplet state with the smallest relative angular momentum R_3=3. In analogy to the superharmonic criterion for Laughlin two-body correlations, their occurrence is related to the form of the three-body pseudopotential at short range. The spectra of a model three-body repulsion are calculated, and the zero-energy Moore--Read ground state, its +-e/4-charged quasiparticles, and the magnetoroton and pair-breaking bands are all identified. The quasiparticles are correctly described by a composite fermion model appropriate for Halperin's p-type pairing with Laughlin correlations between the pairs. However, the Moore--Read ground state, and specially its excitations, have small overlaps with the corresponding Coulomb eigenstates when calculated on a sphere. The reason lies in surface curvature which affects the form of pair pseudopotential for which the "R_3>3" three-body correlations occur. In finite systems, such pseudopotential must be slightly superharmonic at short range (different from Coulomb pseudopotential). However, the connection with the three-body pseudopotential is less size-dependent, suggesting that the Moore--Read state and its excitations are a more accurate description for experimental nu=5/2 states than could be expected from previous calculations.Comment: 12 pages, 12 figures, submitted to PR

The Fermion-Boson Transformation in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a single flux quantum oriented opposite to the applied magnetic field. When the mean field approximation is made in the Haldane spherical geometry, the Fermion angular momentum $l_F$ is replaced by $l_B= l_F-{1\over2}(N-1)$. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical if and only if the pseudopotential is ``harmonic'' in form. However, similar low energy bands of states with Laughlin correlations occur in the two spectra if the interaction has short range. The transformation is used to clarify the relation between Boson and Fermion descriptions of the hierarchy of condensed fractional quantum Hall states.Comment: 5 pages, 4 figures, submitted to Physica

Incompressible states of negatively charged magneto-excitons

We study the system of up to four negatively charged magneto-excitons (X-'s) in the spherical geometry, using the exact-diagonalization techniques. At low energies, X-'s are bound and behave like charged particles without internal dynamics. The pseudopotential describing X-:X- scattering is almost identical to that of electrons and the low-lying few X- states correspond to the few-electron states. The total angular momentum of the ground state depends on the effective filling factor nu and vanishes at its special values. The analogs to the Laughlin nu=1/3 state and the Jain nu=2/5 state of electrons are found. The X- system is predicted to exhibit the fractional quantum Hall effect.Comment: RevTeX + 2 EPS figures formatted in the text with epsf.sty; to appear in Physica

Interaction and dynamical binding of spin waves or excitons in quantum Hall systems

Interaction between spin waves (or excitons) moving in the lowest Landau level is studied using numerical diagonalization. Becuse of complicated statistics obeyed by these composite particles, their effective interaction is completely different from the dipole-dipole interaction predicted in the model of independent (bosonic) waves. In particular, spin waves moving in the same direction attract one another which leads to their dynamical binding. The interaction pseudopotentials V_[up,up](k) and V_[up,down](k) for two spin waves with equal wavevectors k and moving in the same or opposite directions have been calculated and shown to obey power laws V(k) ~ k^alpha at small k. A high value of alpha_[up,up]~4 explains the occurrence of linear bands in the spin excitation spectra of quantum Hall droplets.Comment: 6 pages, 4 figures, submitted to PR