Skyrmions in Higher Landau Levels

We calculate the energies of quasiparticles with large numbers of reversed spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than or equals 1. We find, in contrast with the known result for filling factor equals 1 (k = 0), that these quasiparticles always have higher energy than the fully polarized ones and hence are not the low energy charged excitations, even at small Zeeman energies. It follows that skyrmions are the relevant quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe

Role of disorder in half-filled high Landau levels

We study the effects of disorder on the quantum Hall stripe phases in half-filled high Landau levels using exact numerical diagonalization. We show that, in the presence of weak disorder, a compressible, striped charge density wave, becomes the true ground state. The projected electron density profile resembles that of a smectic liquid. With increasing disorder strength W, we find that there exists a critical value, W_c \sim 0.12 e^2/\epsilon l, where a transition/crossover to an isotropic phase with strong local electron density fluctuations takes place. The many-body density of states are qualitatively distinguishable in these two phases and help elucidate the nature of the transition.Comment: 4 pages, 4 figure

Hund's Rule for Composite Fermions

We consider the ``fractional quantum Hall atom" in the vanishing Zeeman energy limit, and investigate the validity of Hund's maximum-spin rule for interacting electrons in various Landau levels. While it is not valid for {\em electrons} in the lowest Landau level, there are regions of filling factors where it predicts the ground state spin correctly {\em provided it is applied to composite fermions}. The composite fermion theory also reveals a ``self-similar" structure in the filling factor range $4/3>\nu>2/3$.Comment: 10 pages, revte

Wigner Crystals in the lowest Landau level at low filling factors

We report on results of finite-size numerical studies of partially filled lowest Landau level at low electron filling factors. We find convincing evidence suggesting that electrons form Wigner Crystals at sufficiently low filling factors, and the critical filling factor is close to 1/7. At nu=1/7 we find the system undergoes a phase transition from Wigner Crystal to the incompressible Laughlin state when the short-range part of the Coulomb interaction is modified slightly. This transition is either continuous or very weakly first order.Comment: 5 papges RevTex with 8 eps figures embedded in the tex

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

Anisotropic transport in unidirectional lateral superlattice around half-filling of the second Landau level

We have observed marked transport anisotropy in short period (a=92 nm) unidirectional lateral superlattices around filling factors nu=5/2 and 7/2: magnetoresistance shows a sharp peak for current along the modulation grating while a dip appears for current across the grating. By altering the ratio a/l (with l=sqrt{hbar/eB_perp} the magnetic length) via changing the electron density n_e, it is shown that the nu=5/2 anisotropic features appear in the range 6.6 alt a/l alt 7.2 varying their intensities, becoming most conspicuous at a/l simeq 6.7. The peak/dip broadens with temperature roughly preserving its height/depth up to 250 mK. Tilt experiments reveal that the structures are slightly enhanced by an in-plane magnetic field B_| perpendicular to the grating but are almost completely destroyed by B_| parallel to the grating. The observations suggest the stabilization of a unidirectional charge-density-wave or stripe phase by weak external periodic modulation at the second Landau level.Comment: REVTeX, 5 pages, 3 figures, Some minor revisions, Added notes and reference

Theory of the Quantum Hall Smectic Phase II: Microscopic Theory

We present a microscopic derivation of the hydrodynamic theory of the Quantum Hall smectic or stripe phase of a two-dimensional electron gas in a large magnetic field. The effective action of the low energy is derived here from a microscopic picture by integrating out high energy excitations with a scale of the order the cyclotron energy.The remaining low-energy theory can be expressed in terms of two canonically conjugate sets of degrees of freedom: the displacement field, that describes the fluctuations of the shapes of the stripes, and the local charge fluctuations on each stripe.Comment: 20 pages, RevTex, 3 figures, second part of cond-mat/0105448 New and improved Introduction. Final version as it will appear in Physical Review

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

Charge Density Wave-Assisted Tunneling Between Hall Edge States

We study the intra-planar tunneling between quantum Hall samples separated by a quasi one-dimensional barrier, induced through the interaction of edge degrees of freedom with the charge density waves of a Hall crystal defined in a parallel layer. A field theory formulation is set up in terms of bosonic (2+1)-dimensional excitations coupled to (1+1)-dimensional fermions. Parity symmetry is broken at the quantum level by the confinement of soliton-antisoliton pairs near the tunneling region. The usual Peierls argument allows to estimate the critical temperature $T_c$, so that for $T > T_c$ mass corrections due to longitudinal density fluctuations disappear from the edge spectrum. We compute the gap dependence upon the random global phase of the pinned charge density wave, as well as the effects of a voltage bias applied across the tunneling junction.Comment: Additional references + 1 figure + more detailed discussions. To be published in Phys. Rev.

Numerical Test of Disk Trial Wave function for Half-Filled Landau Level

The analyticity of the lowest Landau level wave functions and the relation between filling factor and the total angular momentum severely limits the possible forms of trial wave functions of a disk of electrons subject to a strong perpendicular magnetic field. For N, the number of electrons, up to 12 we have tested these disk trial wave functions for the half filled Landau level using Monte Carlo and exact diagonalization methods. The agreement between the results for the occupation numbers and ground state energies obtained from these two methods is excellent. We have also compared the profile of the occupation number near the edge with that obtained from a field-theoretical method. The results give qualitatively identical edge profiles. Experimental consequences are briefly discussed.Comment: To be published in Phys. Rev. B. 9 pages, 6 figure