Composite Fermions in Modulated Structures: Transport and Surface Acoustic Waves

Motivated by a recent experiment of Willett et al. [Phys. Rev. Lett. 78, 4478 (1997)], we employ semiclassical composite-fermion theory to study the effect of a periodic density modulation on a quantum Hall system near Landau level filling factor nu=1/2. We show that even a weak density modulation leads to dramatic changes in surface-acoustic-wave (SAW) propagation, and propose an explanation for several key features of the experimental observations. We predict that properly arranged dc transport measurements would show a structure similar to that seen in SAW measurements.Comment: Version published in Phys. Rev. Lett. Figures changed to show SAW velocity shift. LaTeX, 5 pages, two included postscript figure

Experimental Demonstration of Fermi Surface Effects at Filling Factor 5/2

Using small wavelength surface acoustic waves (SAW) on ultra-high mobility heterostructures, Fermi surface properties are detected at 5/2 filling factor at temperatures higher than those at which the quantum Hall state forms. An enhanced conductivity is observed at 5/2 by employing sub 0.5 micron wavelength SAW, indicating a quasiparticle mean-free-path substantially smaller than that in the lowest Landau level. These findings are consistent with the presence of a filled Fermi sea of composite fermions, which may pair at lower temperatures to form the 5/2 ground state.Comment: 11 pages, 4 figure

A Fermi Fluid Description of the Half-Filled Landau Level

We present a many-body approach to calculate the ground state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the antisymmetrization operator to the bosonic Laughlin state. Using the classical plasma analogy, we calculate the pair-correlation function, the static structure function and the ground state energy in the thermodynamic limit. These results are in good agreement with the expected behavior at $\nu=\frac12$.Comment: 4 pages, REVTEX, and 4 .ps file

Composite fermions in the Fractional Quantum Hall Effect: Transport at finite wavevector

We consider the conductivity tensor for composite fermions in a close to half-filled Landau band in the temperature regime where the scattering off the potential and the trapped gauge field of random impurities dominates. The Boltzmann equation approach is employed to calculate the quasiclassical transport properties at finite effective magnetic field, wavevector and frequency. We present an exact solution of the kinetic equation for all parameter regimes. Our results allow a consistent description of recently observed surface acoustic wave resonances and other findings.Comment: REVTEX, 4 pages, 1 figur

Dietary flavonoid intake and weight maintenance: three prospective cohorts of 124,086 US men and women followed for up to 24 years

Objective: To examine whether dietary intake of specific flavonoid sub-classes is associated with weight change over time, including flavonols, flavones, flavanones, flavan-3-ols, anthocyanins, and flavonoid polymers. Design: Three prospective cohort studies. Setting: Health professionals in the United States. Participants: 124,086 men and women participating in the Health Professionals Follow-up Study (HPFS), Nurses’ Health Study (NHS), and Nurses’ Health Study II (NHS II). Main outcome measure: Self-reported change in weight over multiple 4-year time intervals between 1986 and 2011. Results: Increased consumption of most flavonoid sub-classes, including flavonols, flavan-3-ols, anthocyanins, and flavonoid polymers was inversely associated with weight change over 4-year time intervals, after adjustment for simultaneous changes in other lifestyle factors including other aspects of diet, smoking status, and physical activity. In the pooled results, the greatest magnitude of association was observed for anthocyanins (-0.22 lbs, 95% CI -0.30 to -0.15 lbs per additional SD/day, 10 mg), flavonoid polymers (-0.18 lbs, 95% CI -0.28 to -0.08 lbs per additional SD/day, 138 mg), and flavonols (-0.16 lbs, 95% CI -0.26 to -0.06 lbs per additional SD/day, 7 mg). After additional adjustment for fiber intake associations remained significant for anthocyanins, proanthocyanidins, and total flavonoid polymers but were attenuated and no longer statistically significant for other sub-classes. Conclusions: Higher intake of foods rich in flavonols, flavan-3-ols, anthocyanins, and flavonoid polymers, may contribute to weight maintenance in adulthood, and may help to refine dietary recommendations for the prevention of obesity and its potential sequelae

Stability and effective masses of composite-fermions in the first and second Landau Level

We propose a measure of the stability of composite fermions (CF's) at even-denominator Landau-level filling fractions. Assuming Landau-level mixing effects are not strong, we show that the CF liquid at $\nu=2+1/2$ in the $n=1$ Landau level cannot exist and relate this to the absence of a hierarchy of incompressible states for filling fractions $2+1/3 < \nu < 2+2/3$. We find that a polarized CF liquid should exist at $\nu=2+1/4$. We also show that, for CF states, the variation with system size of the ground state energy of interacting electrons follows that for non-interacting particles in zero magnetic field. We use this to estimate the CF effective masses.Comment: 9 pages, Revtex, PSIZ-TP-940

Effective mass of composite fermion: a phenomenological fit in with anomalous propagation of surface acoustic wave

We calculate the conductivity associated with the anomalous propagation of a surface acoustic wave above a two-dimensional electron gas at $\nu=1/2$. Murthy-Shankar's middle representation is adopted and a contribution to the response functions beyond the random phase approximation has been taken into account. We give a phenomenological fit for the effective mass of composite fermion in with the experimental data of the anomalous propagation of surface acoustic wave at $\nu=1/2$ and find the phenomenological value of the effective mass is several times larger than the theoretical value $m_{th}^*=6\epsilon/e^2l_{1/2}$ derived from the Hartree-Fock approximation. We compare our phenomenologically fitting composite fermion effective mass with those appeared in the measurements of the activation energy and the Shubnikov-de Haas effect and find that our result is fairly reasonable.Comment: 8 pages, 5 figures, the longer version of cond-mat/9801131 with crucial corrections, accepted for publication by PR

Explanation for the Resistivity Law in Quantum Hall System

We consider a 2D electron system in a strong magnetic field, where the local Hall resistivity $\rho_{xy}(\vec r)$ is a function of position and $\rho_{xx}(\vec r)$ is small compared to $\rho_{xy}$. Particularly if the correlations fall off slowly with distance, or if fluctuations exist on several length scales, one finds that the macroscopic longitudinal resistivity $R_{xx}$ is only weakly dependent on $\rho_{xx}$ and is approximately proportional to the magnitude of fluctuations in $\rho_{xy}$. This may provide an explanation of the empirical law $R_{xx} \propto B \frac{dR_{xy}}{dB}$ where $R_{xy}$ is the Hall resistance, and $B$ is the magnetic field.Comment: 11 pages (REVTeX 3.0). Revised Version. Complete postscript file for this paper is available on the World Wide Web at http://cmtw.harvard.edu/~simon/ ; Preprint number HU-CMT-94S0