Fractional Quantum Hall States of Clustered Composite Fermions

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 chang

Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States

We present an effective Chern-Simons theory for the bulk fully polarized fractional quantum Hall (FQH) hierarchical states constructed as daughters of general states of the Jain series, {\it i. e.} as FQH states of the quasi-particles or quasi-holes of Jain states. We discuss the stability of these new states and present two reasonable stability criteria. We discuss the theory of their edge states which follows naturally from this bulk theory. We construct the operators that create elementary excitations, and discuss the scaling behavior of the tunneling conductance in different situations. Under the assumption that the edge states of these fully polarized hierarchical states are unreconstructed and unresolved, we find that the differential conductance $G$ for tunneling of electrons from a Fermi liquid into {\em any} hierarchical Jain FQH states has the scaling behavior $G\sim V^\alpha$ with the universal exponent $\alpha=1/\nu$, where $\nu$ is the filling fraction of the hierarchical state. Finally, we explore alternative ways of constructing FQH states with the same filling fractions as partially polarized states, and conclude that this is not possible within our approach.Comment: 10 pages, 50 references, no figures; formerly known as "Composite Fermions: The Next Generation(s)" (title changed by the PRB thought police). This version has more references and a discussion of the stability of the new states. Published version. One erroneous reference is correcte

Random Field Models for Relaxor Ferroelectric Behavior

Heat bath Monte Carlo simulations have been used to study a four-state clock model with a type of random field on simple cubic lattices. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a random field which consists of adding an energy $D$ to one of the four spin states, chosen randomly at each site. This Ashkin-Teller-like model does not separate; the two random-field Ising model components are coupled. When $D / J = 3$, the ground states of the model remain fully aligned. When $D / J \ge 4$, a different type of ground state is found, in which the occupation of two of the four spin states is close to 50%, and the other two are nearly absent. This means that one of the Ising components is almost completely ordered, while the other one has only short-range correlations. A large peak in the structure factor $S (k)$ appears at small $k$ for temperatures well above the transition to long-range order, and the appearance of this peak is associated with slow, "glassy" dynamics. The phase transition into the state where one Ising component is long-range ordered appears to be first order, but the latent heat is very small.Comment: 7 pages + 12 eps figures, to appear in Phys Rev

Fractional-quantum-Hall edge electrons and Fermi statistics

We address the quantum statistics of electrons created in the low-energy edge-state Hilbert space sector of incompressible fractional quantum Hall states, considering the possibility that they may not satisfy Fermi statistics. We argue that this property is not a priori obvious, and present numerical evidence based on finite-size exact-diagonalization calculations that it does not hold in general. We discuss different possible forms for the expression for the electron creation operator in terms of edge boson fields and show that none are consistent with our numerical results on finite-size filling-factor-2/5 states with short-range electron-electron interactions. Finally, we discuss the current body of experimental results on tunneling into quantum Hall edges in the context of this result.Comment: 9 pages, 1 figure, RevTex

Momentum-Resolved Tunneling into Fractional Quantum Hall Edges

Tunneling from a two-dimensional contact into quantum-Hall edges is considered theoretically for a case where the barrier is extended, uniform, and parallel to the edge. In contrast to previously realized tunneling geometries, details of the microscopic edge structure are exhibited directly in the voltage and magnetic-field dependence of the differential tunneling conductance. In particular, it is possible to measure the dispersion of the edge-magnetoplasmon mode, and the existence of additional, sometimes counterpropagating, edge-excitation branches could be detected.Comment: 4 pages, 3 figures, RevTex

Energy, interaction, and photoluminescence of spin-reversed quasielectrons in fractional quantum Hall systems

The energy and photoluminescence spectra of a two-dimensional electron gas in the fractional quantum Hall regime are studied. The single-particle properties of reversed-spin quasielectrons (QE$_{\rm R}$'s) as well as the pseudopotentials of their interaction with one another and with Laughlin quasielectrons (QE's) and quasiholes (QH's) are calculated. Based on the short-range character of the QE$_{\rm R}$--QE$_{\rm R}$ and QE$_{\rm R}$--QE repulsion, the partially unpolarized incompressible states at the filling factors $\nu={4\over11}$ and ${5\over13}$ are postulated within Haldane's hierarchy scheme. To describe photoluminescence, the family of bound $h($QE$_{\rm R})_n$ states of a valence hole $h$ and $n$ QE$_{\rm R}$'s are predicted in analogy to the found earlier fractionally charged excitons $h$QE$_n$. The binding energy and optical selection rules for both families are compared. The $h$QE$_{\rm R}$ is found radiative in contrast to the dark $h$QE, and the $h($QE$_{\rm R})_2$ is found non-radiative in contrast to the bright $h$QE$_2$.Comment: 9 pages, 6 figure

Topological Defects and Non-homogeneous Melting of Large 2D Coulomb Clusters

The configurational and melting properties of large two-dimensional clusters of charged classical particles interacting with each other via the Coulomb potential are investigated through the Monte Carlo simulation technique. The particles are confined by a harmonic potential. For a large number of particles in the cluster (N>150) the configuration is determined by two competing effects, namely in the center a hexagonal lattice is formed, which is the groundstate for an infinite 2D system, and the confinement which imposes its circular symmetry on the outer edge. As a result a hexagonal Wigner lattice is formed in the central area while at the border of the cluster the particles are arranged in rings. In the transition region defects appear as dislocations and disclinations at the six corners of the hexagonal-shaped inner domain. Many different arrangements and type of defects are possible as metastable configurations with a slightly higher energy. The particles motion is found to be strongly related to the topological structure. Our results clearly show that the melting of the clusters starts near the geometry induced defects, and that three different melting temperatures can be defined corresponding to the melting of different regions in the cluster.Comment: 7 pages, 11 figures, submitted to Phys. Rev.

Edge reconstruction in the fractional quantum Hall regime

The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects like layer thickness and Landau level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes arise for both incompressible and compressible states. These additional modes couple to electromagnetic fields and thus can be detected in microwave conductivity measurements. They are also expected to affect the exponent of electron Green's function, which has been measured in tunneling experiments. We have studied in this work the electric dipole spectral function that is directly related to the microwave conductivity measurement. Our results are consistent with the enhanced microwave conductivity observed in experiments performed on samples with an array of antidots at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the single electron spectral function at the edge.Comment: 19 pages, 12 figure

Structures for Interacting Composite Fermions: Stripes, Bubbles, and Fractional Quantum Hall Effect

Much of the present day qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the interactions between composite fermions altogether. For example the fractional quantum Hall effect at $\nu=n/(2pn\pm 1)$ corresponds to filled composite-fermion Landau levels,and the compressible state at $\nu=1/2p$ to the Fermi sea of composite fermions. Away from these filling factors, the residual interactions between composite fermions will determine the nature of the ground state. In this article, a model is constructed for the residual interaction between composite fermions, and various possible states are considered in a variational approach. Our study suggests formation of composite-fermion stripes, bubble crystals, as well as fractional quantum Hall states for appropriate situations.Comment: 16 pages, 7 figure

Vortex dynamics for two-dimensional XY models

Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent $z$ in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature $T^{CG}$ and the vortex renormalization given by the dielectric constant $\tilde\epsilon$) $z=1/\tilde{\epsilon}T^{CG}-2\geq 2$ both for RSJ and TDGL and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio