Dynamical Kohn Anomaly in Surface Acoustic Wave Response in Quantum Hall Systems Near ν=1/2\nu = 1/2

The dynamical analog of the Kohn Anomaly image of the Fermi Surface is demonstrated for the response functions to the surface acoustic waves in Quantum Hall Systems near $\nu = 1/2$. Kinks appear in the velocity shift $Delta s/s$ and attenuation coefficient $\Gamma$. The effect is considerably enhanced under periodic modulation and should be observable.Comment: 5 pages, 2 figures, the published versio

Theory of Magneto--Acoustic Transport in Modulated Quantum Hall Systems Near ν=1/2\nu=1/2

Motivated by the experimental results of Willett et al [Phys.Rev. Lett., {\bf 78}, 4478 (1997)] we develop a magneto-transport theory for the response of a two dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near Landau level filling factor $\nu = 1/2$ to the surface acoustic wave (SAW) in the presence of an added periodic density modulation. We assume there exists a Composite Fermion Fermi Surface (CF-FS) at $\nu = 1/2$, and we show that the deformation of the (CF-FS) due to the density modulation can be at the origin of the observed transport anomalies for the experimental conditions. Our analysis is carried out particularly for the non-local case which corresponds to the SAW experiments. We introduce a new model of a deformed CF-FS. The model permits us to explain anomalous features of the response of the modulated 2DEG to the SAW near $\nu = 1/2:$ namely the nonlinear wave vector dependence of the electron conductivity, the appearance of peaks in the SAW velocity shift and attenuation and the anisotropy of the effect, all of which originate from contributions to the conductivity tensor due to the regions of the CF-FS which are flattened by the applied modulation.Comment: 13 pages, 4 figures, the published versio

Pulsed Magnetic Field Measurements of the Composite Fermion Effective Mass

Magnetotransport measurements of Composite Fermions (CF) are reported in 50 T pulsed magnetic fields. The CF effective mass is found to increase approximately linearly with the effective field $B^*$, in agreement with our earlier work at lower fields. For a $B^*$ of 14 T it reaches $1.6m_e$, over 20 times the band edge electron mass. Data from all fractions are unified by the single parameter $B^*$ for all the samples studied over a wide range of electron densities. The energy gap is found to increase like $\sqrt{B^*}$ at high fields.Comment: Has final table, will LaTeX without error

Composite Fermions and the Energy Gap in the Fractional Quantum Hall Effect

The energy gaps for the fractional quantum Hall effect at filling fractions 1/3, 1/5, and 1/7 have been calculated by variational Monte Carlo using Jain's composite fermion wave functions before and after projection onto the lowest Landau level. Before projection there is a contribution to the energy gaps from the first excited Landau level. After projection this contribution vanishes, the quasielectron charge becomes more localized, and the Coulomb energy contribution increases. The projected gaps agree well with previous calculations, lending support to the composite fermion theory.Comment: 12 pages, Revtex 3.0, 2 compressed and uuencoded postscript figures appended, NHMFL-94-062

Measurements of the Composite Fermion masses from the spin polarization of 2-D electrons in the region 1<ν<21<\nu<2

Measurements of the reflectivity of a 2-D electron gas are used to deduce the polarization of the Composite Fermion hole system formed for Landau level occupancies in the regime 1<\nu<2. The measurements are consistent with the formation of a mixed spin CF system and allow the density of states or `polarization' effective mass of the CF holes to be determined. The mass values at \nu=3/2 are found to be ~1.9m_{e} for electron densities of 4.4 x 10^{11} cm^{-2}, which is significantly larger than those found from measurements of the energy gaps at finite values of effective magnetic field.Comment: 4 pages, 3 fig

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.

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

Unrestricted Hartree-Fock theory of Wigner crystals

We demonstrate that unrestricted Hartree-Fock theory applied to electrons in a uniform potential has stable Wigner crystal solutions for $r_s \geq 1.44$ in two dimensions and $r_s \geq 4.5$ in three dimensions. The correlation energies of the Wigner crystal phases are considerably smaller than those of the fluid phases at the same density.Comment: 4 pages, 5 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

Spin-pairing instabilities at the coincidence of two Landau levels

The effect of interactions near the coincidence of two Landau levels with opposite spins at filling factor 1/2 is investigated. By mapping to Composite Fermions it is shown that the fluctuations of the gauge field induces an effective attractive Fermion interaction. This can lead to a spin-singlet ground state that is separated from the excited states by a gap. The magnitude of the gap is evaluated. The results are consistent with the recently observed half-polarized states in the FQHE at a fixed filling factor. It is suggested that similar anomalies exist for other spin configurations in degenerate spin-up and spin-down Landau levels. An experiment for testing the spin-singlet state is proposed.Comment: to be published in Physical Review