Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux

The semiclassical quantization rule is derived for a system with a spherically symmetric potential $V(r) \sim r^{\nu}$ $(-2<\nu <\infty)$ and an Aharonov-Bohm magnetic flux. Numerical results are presented and compared with known results for models with $\nu = -1,0,2,\infty$. It is shown that the results provided by our method are in good agreement with previous results. One expects that the semiclassical quantization rule shown in this paper will provide a good approximation for all principle quantum number even the rule is derived in the large principal quantum number limit $n \gg 1$. We also discuss the power parameter $\nu$ dependence of the energy spectra pattern in this paper.Comment: 13 pages, 4 figures, some typos correcte

Electromagnetic field angular momentum in condensed matter systems

Various electromagnetic systems can carry an angular momentum in their {\bf E} and {\bf B} fields. The electromagnetic field angular momentum (EMAM) of these systems can combine with the spin angular momentum to give composite fermions or composite bosons. In this paper we examine the possiblity that an EMAM could provide an explanation of the fractional quantum Hall effect (FQHE) which is complimentary to the Chern-Simons explanation. We also examine a toy model of a non-BCS superconductor (e.g. high $T_c$ superconductors) in terms of an EMAM. The models presented give a common, simple picture of these two systems in terms of an EMAM. The presence of an EMAM in these systems might be tested through the observation of the decay modes of a charged, spin zero unstable particle inside one of these systems.Comment: 17 pages, no figures, to be published in Phys. Rev.

Quasi-Fermi Distribution and Resonant Tunneling of Quasiparticles with Fractional Charges

We study the resonant tunneling of quasiparticles through an impurity between the edges of a Fractional Quantum Hall sample. We show that the one-particle momentum distribution of fractionally charged edge quasiparticles has a quasi-Fermi character. The density of states near the quasi-Fermi energy at zero temperature is singular due to the statistical interaction of quasiparticles. Another effect of this interaction is a new selection rule for the resonant tunneling of fractionally charged quasiparticles: the resonance is suppressed unless an integer number of {\em electrons} occupies the impurity. It allows a new explanation of the scaling behavior observed in the mesoscopic fluctuations of the conductivity in the FQHE.Comment: 7 pages, REVTeX 3.0, Preprint SU-ITP-93-1

Invariant structure of the hierarchy theory of fractional quantum Hall states with spin

We describe the invariant structure common to abelian fractional quantum Hall systems with spin. It appears in a generalization of the lattice description of the polarized hierarchy that encompasses both partially polarized and unpolarized ground state systems. We formulate, using the spin-charge decomposition, conditions that should be satisfied so that the description is SU(2) invariant. In the case of the spin- singlet hierarchy construction, we find that there are as many SU(2) symmetries as there are levels in the construction. We show the existence of a spin and charge lattice for the systems with spin. The ``gluing'' of the charge and spin degrees of freedom in their bulk is described by the gluing theory of lattices.Comment: 21 pages, LaTex, Submitted to Phys. Rev.

Magnetization and Level Statistics at Quantum Hall Liquid-Insulator Transition in the Lattice Model

Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.Comment: 4 pages, 6 figure

Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level

Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson system in a uniform external field such that there is one flux quantum per particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at half-filling to a boson system at integer filling fails.Comment: 13 pages latex with revtex. To be published in Phys. Rev.

Thermodynamics of an Anyon System

We examine the thermal behavior of a relativistic anyon system, dynamically realized by coupling a charged massive spin-1 field to a Chern-Simons gauge field. We calculate the free energy (to the next leading order), from which all thermodynamic quantities can be determined. As examples, the dependence of particle density on the anyon statistics and the anyon anti-anyon interference in the ideal gas are exhibited. We also calculate two and three-point correlation functions, and uncover certain physical features of the system in thermal equilibrium.Comment: 18 pages; in latex; to be published in Phys. Rev.

Weak localization of disordered quasiparticles in the mixed superconducting state

Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear sigma model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field H_c1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for the field dependence of the thermal conductivity seen in recent high-T_c experiments by Aubin et al.Comment: RevTex, 8 pages, 1 eps figure, typos correcte

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