Statistics of skyrmions in Quantum Hall systems

We analyze statistical interactions of skyrmions in the quantum Hall system near a critical filling fraction in the framework of the Ginzburg-Landau model. The phase picked up by the wave-function during an exchange of two skyrmions close to $\nu=1/(2n+1)$ is $\pi[S+1/2(2n+1)]$, where $S$ is the skyrmion's spin. In the same setting an exchange of two fully polarized vortices gives rise to the phase $\pi/(2n+1)$. Skyrmions with odd and even numbers of reversed spins have different quantum statistics. Condensation of skyrmions with an even number of reversed spins leads to filling fractions with odd denominators, while condensation of those with an odd number of reversed spins gives rise to filling fractions with even denominators.Comment: 6 pages in Latex. addendum - skyrmions with odd or even number of reversed spins have different quantum statistics. They condense to form respectively even or odd denominator filling fraction state

Quantum fluctuations of classical skyrmions in quantum Hall Ferromagnets

In this article, we discuss the effect of the zero point quantum fluctuations to improve the results of the minimal field theory which has been applied to study %SMG the skyrmions in the quantum Hall systems. Our calculation which is based on the semiclassical treatment of the quantum fluctuations, shows that the one-loop quantum correction provides more accurate results for the minimal field theory.Comment: A few errors are corrected. Accepted for publication in Rapid Communication, Phys. Rev.

Massive skyrmions in quantum Hall ferromagnets

We apply the theory of elasticity to study the effects of skyrmion mass on lattice dynamics in quantum Hall systems. We find that massive Skyrme lattices behave like a Wigner crystal in the presence of a uniform perpendicular magnetic field. We make a comparison with the microscopic Hartree-Fock results to characterize the mass of quantum Hall skyrmions at $\nu=1$ and investigate how the low temperature phase of Skyrme lattices may be affected by the skyrmion mass.Comment: 6 pages and 2 figure

Spin symmetry breaking in bilayer quantum Hall systems

Based on the construction of generalized Halperin wave functions, we predict the possible existence of a large class of broken spin symmetry states in bilayer quantum Hall structures, generalizing the recently suggested canted antiferromgnetic phase to many fractional fillings. We develop the appropriate Chern-Simons theory, and establish explicitly that the low-lying neutral excitation is a Goldstone mode and that the charged excitations are bimerons with continuously tunable (through the canted antiferromagnetic order parameter) electric charge on the individual merons.Comment: 4 page

Resonant Tunneling Between Quantum Hall Edge States

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for $\nu = 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.Comment: 14 pages , revtex , IUCM93-00

Edge and Bulk of the Fractional Quantum Hall Liquids

An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this boundary condition, the action remains gauge invariant and the edge modes are naturally derived. We find that the integer coupling matrix $K$ should satisfy the condition $\sum_I(K^{-1})_{IJ} = \nu/m$ ($\nu$: filling of Landau levels, $m$: the number of gauge fields ) for the quantum Hall liquids. Then the Hall conductance is always quantized irrespective of the detailed dynamics or the randomness at the edge.Comment: 13 pages, REVTEX, one figure appended as a postscript fil

Current and charge distributions of the fractional quantum Hall liquids with edges

An effective Chern-Simons theory for the quantum Hall states with edges is studied by treating the edge and bulk properties in a unified fashion. An exact steady-state solution is obtained for a half-plane geometry using the Wiener-Hopf method. For a Hall bar with finite width, it is proved that the charge and current distributions do not have a diverging singularity. It is shown that there exists only a single mode even for the hierarchical states, and the mode is not localized exponentially near the edges. Thus this result differs from the edge picture in which electrons are treated as strictly one dimensional chiral Luttinger liquids.Comment: 21 pages, REV TeX fil

Hartree-Fock Theory of Skyrmions in Quantum Hall Ferromagnets

We report on a study of the charged-skyrmion or spin-texture excitations which occur in quantum Hall ferromagnets near odd Landau level filling factors. Particle-hole symmetry is used to relate the spin-quantum numbers of charged particle and hole excitations and neutral particle-hole pair excitations. Hartree-Fock theory is used to provide quantitative estimates of the energies of these excitations and their dependence on Zeeman coupling strength, Landau level quantum numbers, and the thicknesses of the two-dimensional electron layers. For the case of $\nu$ near three we suggest the possibility of first order phase transitions with increasing Zeeman coupling strength from a many skyrmion state to one with many maximally spin-polarized quasiparticles.Comment: 26 pages, 10 figure

Square to stripe transition and superlattice patterns in vertically oscillated granular layers

We investigated the physical mechanism for the pattern transition from square lattice to stripes, which appears in vertically oscillating granular layers. We present a continuum model to show that the transition depends on the competition between inertial force and local saturation of transport. By introducing multiple free-flight times, this model further enables us to analyze the formation of superlattices as well as hexagonal lattice

Skyrmion Excitations in Quantum Hall Systems

Using finite size calculations on the surface of a sphere we study the topological (skyrmion) excitation in quantum Hall system with spin degree of freedom at filling factors around $\nu=1$. In the absence of Zeeman energy, we find, in systems with one quasi-particle or one quasi-hole, the lowest energy band consists of states with $L=S$, where $L$ and $S$ are the total orbital and spin angular momentum. These different spin states are almost degenerate in the thermodynamic limit and their symmetry-breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron interaction and the skyrmion shrinks to a spin texture of finite size. We have calculated the energy gap of the system at infinite wave vector limit as a function of the Zeeman energy and find there are kinks in the energy gap associated with the shrinking of the size of the skyrmion. breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electronComment: 4 pages, 5 postscript figures available upon reques