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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 figures

The correlations that give rise to incompressible quantum liquid (IQL) states in fractional quantum Hall systems are determined by the pseudopotential $V(\mathcal R)$ describing the interaction of a pair of Fermions in a degenerate Landau level (LL) as a function of relative pair angular momentum $\mathcal R$. $V(\mathcal R)$ is known for a number of different Fermion systems, e.g. electrons in the lowest Landau level (LL0) or the first excited Landau level (LL1), and for quasiparticles of Laughlin-Jain IQL states. Laughlin correlations, the avoidance of pair states with the smallest values of $\mathcal R$, occur only when $V(\mathcal R)$ satisfies certain conditions. We show that Jain's composite Fermion (CF) picture is valid only if the conditions necessary for Laughlin correlations are satisfied, and we present a rigorous justification of the CF picture without the need of introducing an "irrelevant" mean field energy scale. Electrons in LL1 and quasielectrons in IQL states (e.g. QEs in CF LL1) do not necessarily support Laughlin correlations. Numerical diagonalization studies for small systems of Fermions (electrons in LL0 or in LL1, and QEs in CF LL1), with the use appropriate pseudopotentials $V(\mathcal R)$, show clear evidence for different types of correlations. The relation between LL degeneracy $g=2\ell+1$ and number of Fermions $N$ at which IQL states are found is known for a limited range of $N$ values. However, no simple intuitive models that we have tried satisfactorily describe all of the systems we have studied. Successes and shortcomings of some simple models are discussed, and suggestions for further investigation are made., Comment: 49 pages, 45 figures

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 figures

Spin polarization of the "second generation" nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is determined for GaAs structures of different width and electron concentration. Transition between the polarized and partially unpolarized states with distinct composite fermion correlations is predicted for realistic parameters., Comment: 5 pages, 3 figures

The nu=5/2 fractional quantum Hall state is studied numerically, directly including the effects of electron scattering between neighboring Landau levels. Significant reduction of the excitation gap caused by the LL mixing explains the discrepancy between earlier calculations and experiments. On the other hand, LL mixing also considerably reduces overlaps with the Moore--Read wavefunction, raising a question of the actual realization of nonabelian quasiparticles in present experiments., Comment: 4 pages, 4 figures

Binding energies of negative and positive trions in doped GaAs quantum wells in high magnetic fields are studied by exact numerical diagonalization in spherical geometry. Compared to earlier calculations, finite width of the quantum well and its asymmetry caused by one-sided doping are both fully taken into account by using self-consistent subband wave functions in the integration of Coulomb matrix elements, and by inclusion of higher subbands along with several Landau levels in the Hilbert space. Detailed analysis of the accuracy and convergence of the exact diagonalization scheme is presented, including dependence on Landau level and subband mixing, sensitivity to the (not well known) single-particle spectrum in the valence band, and the estimate of finite-size errors. The main results are the exciton dispersion and trion binding energy spectrum calculated as a function of the magnetic field, quantum well width, electron concentration, and the presence of an ionized impurity. As a complementary approach, a combination of the exact diagonalization in the quantum well plane and the variational calculation in the normal direction is used as well., Comment: 14 pages, 18 figures

Two- and three-body correlations of incompressible quantum liquids are studied numerically. Pairing of composite fermions (CFs) in the 1/3-filled second CF Landau level is found at nu_e=4/11. It is explained by reduced short-range repulsion due to ring-like single-particle charge distribution. Although Moore-Read state of CFs is unstable in the 1/2-filled second CF level, condensation of its quasiholes is a possible origin of incompressibility at nu_e=4/11. Electron pairing occurs at nu_e=7/3 and 13/3, but with different pair-pair correlations. Signatures of triplets are found at higher fillings., Comment: 4 pages

Photoluminescence (PL) has been used to study two-dimensional incompressible electron liquids in high magnetic fields for nearly two decades. However, some of the observed anomalies coincident with the fractional quantum Hall effect are still unexplained. We show that emission in these systems occurs from fractionally charged "quasiexciton" states formed from trions correlated with the surrounding electrons. Their binding and recombination depend on the state of both the electron liquid and the involved trion, predicting discontinuities in PL and sensitivity to sample parameters., Comment: 4 pages, 4 figures

Pair-distribution functions g(r) of Laughlin quasielectrons (composite fermions in their second Landau level) are calculated in the fractional quantum Hall states at electron filling factors nu_e=4/11 and 3/8. A shoulder in g(r) is found, supporting the idea of cluster formation. The intra- and inter-cluster contributions to g(r) are identified, largely independent of nu_e. The average cluster sizes are estimated; pairs and triplets of quasielectrons are suggested at nu_e=4/11 and 3/8, respectively., Comment: submitted to PRB

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 PRB

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 PRB

The residual interactions between Laughlin quasiparticles can be obtained from exact numerical diagonalization studies of small systems. The pseudopotentials V_QP(R)$ describing the energy of interaction of QE's (or QH's) as a function of their "relative angular momentum" R cannot support Laughlin correlations at certain QP filling factors (e.g., nu_QE}=1/3 and nu_QH=1/5). Because of this the novel condensed quantum fluid states observed at nu=4/11, 4/13 and other filling fractions cannot possibly be spin polarized Laughlin correlated QP states of the composite Fermion hierarchy. Pairing of the QP's clearly must occur, but the exact nature of the incompressible ground states is not completely clear., Comment: 5 pages, 2 figures, accepted for Solid State Commun

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high density the QE's form pairs or larger clusters. This behavior, opposite to Laughlin correlations, invalidates the (sometimes invoked) reapplication of the composite fermion picture to the individual QE's. The series of finite-size incompressible ground states are identified at the QE filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4, 1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states were recently discovered experimentally. Detailed analysis indicates that QE or QH correlations in these states are different from those of well-known FQH electron states (e.g., Laughlin or Moore-Read states), leaving the origin of their incompressibility uncertain. Halperin's idea of Laughlin states of QP pairs is also explored, but is does not seem adequate., Comment: 14 pages, 9 figures; revision: 1 new figure, some new references, some new data, title change

The electronic properties of quasi two-dimensional multicomponent systems are investigated in the presence of a perpendicular magnetic field. The effects of the presence of a few valence band holes on the properties of quantum Hall systems are examined by analyzing the results of exact numerical diagonalization of small electron-hole systems confined to the spherical surface. The novel type of elementary excitations, the angular momenta, binding energies, interaction pseudopotentials, and effects on the photoluminescence spectrum are presented., Comment: 31 pages, 8 figures, review article

Fractional quantum Hall (FQH) states have recently been observed at unexpected values of the filling factor nu. Here we interpret these states as a novel family of FQH states involving pairing correlations rather than Laughlin correlations among the quasiparticles (QP's). The correlations depend upon the behavior of the QP-QP pseudopotential V_QP(L'), the interaction energy of a pair as a function of the pair angular momentum L'. This behavior, known from numerical studies of small systems, is used to demonstrate that pairing correlations give rise to FQH states at the experimentally observed values of nu., Comment: to appear in Physics Letters A

The formation and various possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively and positively charged quasiparticles (e.g., conduction electrons and valence holes, reversed-spin electrons and spin holes, Laughlin quasielectrons and quasiholes, composite fermions) that occur in an electron system under specific conditions (e.g., electron density, well width, electric and magnetic fields, or hydrostatic pressure). The examples of such bound states are interband neutral and charged excitons, fractionally charged "anyon excitons", spin waves, skyrmions, or "skyrmion excitons". Their possible decay processes include radiative recombination, experimentally observed in photoluminescence or far infrared emission, or spin transitions, important in the context of nuclear spin relaxation., Comment: 15th Int. Conf. on High Magnetic Fields in Semiconductor Physics; Clarendon Laboratory, Oxford, August 5-9, 2002; 12 pages, 12 figures

The formation and possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively and positively charged quasiparticles (e.g., conduction electrons and valence holes, reversed-spin electrons and spin holes, Laughlin quasielectrons and quasiholes, composite Fermions) that can occur in a 2D electron in the presence of a strong magnetic field. Examples of such bound states are interband neutral and charged excitons, fractionally charged "anyon excitons", spin waves, skyrmions, or "skyrmion excitons". Possible decay processes include radiative recombination, experimentally observed in photoluminescence or spin transitions, important in the context of nuclear spin relaxation., Comment: XXVI International Workshop on Condensed Matter Theories; Luso, Portugal, September 2-7, 2002; 10 pages, 5 figures

The occurrence of incompressible quantum fluid states of a two dimensional system is a result of electron--electron interactions in a highly degenerate fractionally filled Landau level. Novel quasiparticles (QP's) called composite Fermions (CF's) have allowed a simple single particle description of the most prominent incompressible states. Residual interactions among these QP's are investigated. These interactions determine the type of "daughter states" that can occur at the next generation. We demonstrate that at certain values of the QP filling factor nu_QP, Laughlin correlations among the QP's give rise to states of the standard CF hierarchy. At other values of nu_QP pairing of QP's is found leading to a novel hierarchy of incompressible states., Comment: Int. School of Physics "Enrico Fermi"; Varenna, Italy, 7/29-8/8/2003; 29 pages, 10 figures

From the analysis of their interaction pseudopotentials, it is argued that (at certain filling factors) Laughlin quasiparticles can form pairs. It is further proposed that such pairs could have Laughlin correlations with one another and form condensed states of a new type. The sequence of fractions corresponding to these states includes all new fractions observed recently in experiment (e.g., \nu=5/13, 3/8, or 4/11)., Comment: XXXII Int. School on the Physics of Semiconducting Compounds; Jaszowiec, Poland, May 30 - June 6, 2003; 4 pages, 0 figures

The mean field (MF) composite Fermion (CF) picture successfully predicts the low-lying bands of states of fractional quantum Hall systems. This success cannot be attributed to the originally proposed cancellation between Coulomb and Chern--Simons interactions beyond the mean field and solely depends on the short range of the repulsive Coulomb pseudopotential in the lowest Landau level (LL). The class of pseudopotentials is defined for which the MFCF picture can be applied. The success or failure of the MFCF picture in various systems (electrons in the lowest and excited LL's, Laughlin quasiparticles) is explained., Comment: VII International School on Theoretical Physics: Symmetry and Structural Properties of Condensed Matter Myczkowce, Poland, September 11-18, 2002

A novel hierarchy of fractional quantum Hall (FQH) states in the lowest Landau level (LL) is proposed to explain recently observed FQH fractions such as nu=5/13, 3/8, or 4/11. Based on the analysis of their interaction pseudopotentials, it is argued that the Laughlin quasiparticles (particles/holes in a partially filled composite fermion LL) form pairs. These pairs are proposed to have Laughlin correlations with one another and to form condensed states at a sequence of fractions which includes all new fractions observed in experiment., Comment: 4 pages, 2 figures

If the Zeeman energy is small, the lowest energy excitations of a two dimensional electron gas at filling factor nu=1 are spin waves (spin flip excitations). At nu slightly larger (smaller) than unity, reversed spin electrons (spin holes) can form bound states with K spin waves that are known as skyrmions, S_K^- (antiskyrmions, S_K^+). It is suggested in this work that a valence hole can also bind K spin waves to form an excitonic complex X_K^+, analogous to the S_K^+. One spin hole of the S_K^+ is simply replaced by the valence hole. At nu<=1, a small number of S_K^+'s are present before introduction of the valence hole. The (S_K^+)-(X_K^+) repulsion leads to correlations and photoluminescence similar to those of a dilute electron-(charged-exciton) (e-X^-) system at nu<=1/3. At nu>=1, the (S_K^-)-(X_K^+) attraction can potentially lead to different behavior., Comment: 9 pages, 4 figures, invited lecture at SID8, Buffalo (2002)

We report on the numerical study of the relaxation rates of nuclear spins coupled through the hyperfine interaction to a two dimensional electron gas (2DEG) at magnetic fields corresponding to both fractional and integral Landau level (LL) fillings nu. The Hamiltonians of up to 20 interacting electrons are diagonalized exactly in the spherical geometry, neglecting finite layer width, disorder, and LL mixing. The spectral functions tau^-1(E) describing response of the 2DEG to the reversal of an embedded localized spin are calculated. In a (locally) incompressible nu=1 or 1/3 state, the finite Coulomb energy of short spin waves, together with the small nuclear Zeeman energy, prevent nuclear spin relaxation even in the limit of vanishing electron Zeeman energy E_Z. However, we find that the nuclear spins can couple to the internal excitations of mobile finite-size skyrmions that appear in the 2DEG at sufficiently low E_Z and at nu slightly different from 1 or 1/3. The experimentally observed dependence of nuclear spin relaxation rate on E_Z and nu is qualitatively explained in terms of the occurrence of skyrmions and antiskyrmions of various topological charge., Comment: 10 pages, 7 figures

The inter-Landau-level spin excitations of quantum Hall states at filling factors nu=2 and 4/3 are investigated by exact numerical diagonalization for the situation in which the cyclotron (hbar*omega_c) and Zeeman (E_Z) splittings are comparable. The relevant quasiparticles and their interactions are studied, including stable spin wave and skyrmion bound states. For nu=2, a spin instability at a finite value of epsilon=hbar*omega_c-E_Z leads to an abrupt paramagnetic to ferromagnetic transition, in agreement with the mean-field approximation. However, for nu=4/3 a new and unexpected quantum phase transition is found which involves a gradual change from paramagnetic to ferromagnetic occupancy of the partially filled Landau level as epsilon is decreased., Comment: 4 pages, 5 figures, submitted to Phys.Rev.Lett

Results are presented of detailed numerical calculations for the spin excitation spectra of a two-dimensional electron gas confined in a quantum well of finite width w, at magnetic fields corresponding to the fractional and integral fillings of the lowest and of excited Landau levels. Spin waves and skyrmions are identified, and their mutual interactions are studied at filling factors nu=1/3, 1, 3, and 5. The smallest skyrmions at nu=1/3 are equivalent to composite fermion charged excitons X_CF^(+/-). Bose condensates of nearly noninteracting spin waves and Laughlin correlations between finite-size skyrmions are found at nu=1 and 1/3 and, for w larger than about two magnetic lengths, also at nu=3 and 5. A general criterion for the occurrence of skyrmions at odd integral fillings and at Laughlin fractional fillings of the lowest Landau level is given in terms of the interaction pseudopotentials. This explains the dependence of skyrmion states on w observed in excited Landau levels., Comment: 12 pages, 14 figures, submitted to Phys. Rev. B

Numerical results are presented for the spin excitations of a two-dimensional electron gas confined to a quantum well of width w. Spin waves and charged skyrmion excitations are studied for filling factors nu=1, 3, and 1/3. Phase diagrams for the occurrence of skyrmions of different size as a function of w and the Zeeman energy are calculated. For nu=3, skyrmions occur only if w is larger than about twice the magnetic length. A general necessary condition on the interaction pseudopotential for the occurrence of stable skyrmion states is proposed., Comment: 4 pages, 6 figures, submitted to Solid State Commun

The form of electron correlations in a partially filled degenerate Landau level (LL) is related to the behavior of the anharmonic part of the interaction pseudopotential. Unlike in the lowest LL, the pseudopotential in the first excited LL is harmonic at short range. As a result, the incompressible states in this LL have different correlations, occur at different filling factors nu, and cannot be described by a composite fermion model. The series of Laughlin-correlated states of electron pairs is proposed at nu=2+2/(q_2+2) with integer q_2. It includes Moore-Read nu=5/2 state and the nu=7/3 state. Despite coincidence of the values of nu, the latter state has different correlations than Laughlin state of single electrons at nu=1/3 and, in finite systems, occurs at a different LL degeneracy (flux)., Comment: 4 pages, 5 figures, paper for EP2DS14

The energy, interaction, and optical properties of reversed-spin quasielectrons (QE_R's) in fractional quantum Hall systems are studied. Based on the short range of the QE_R-QE_R repulsion, a partially unpolarized incompressible nu=4/11 state is postulated within Haldane hierarchy scheme. To describe photoluminescence, a reversed-spin fractionally charged exciton hQE_R (QE_R bound to a valence hole h) is predicted. In contrast to its spin-polarized analog, hQE_R is strongly bound and radiative., Comment: 4 pages, 2 figures, paper for EP2DS14