Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $\lambda = (e^2/\epsilon l_0)/\hbar\omega_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions $\nu=1/3$ and 1/5 using a modified version of Jain's composite fermion wave functions. These wave functions exploit the Landau level mixing already present in composite fermion wave functions by introducing a partial Landau level projection operator. Results for the energy gaps are consistent with experimental observations in $n$-type GaAs, but we conclude that Landau level mixing alone cannot account for the significantly smaller energy gaps observed in $p$-type systems.Comment: 11 pages, RevTex, 2 figures in compressed tar .ps forma

Mixed States of Composite Fermions Carrying Two and Four Vortices

There now exists preliminary experimental evidence for some fractions, such as $\nu$ = 4/11 and 5/13, that do not belong to any of the sequences $\nu=n/(2pn\pm 1)$, $p$ and $n$ being integers. We propose that these states are mixed states of composite fermions of different flavors, for example, composite fermions carrying two and four vortices. We also obtain an estimate of the lowest-excitation dispersion curve as well as the transport gap; the gaps for 4/11 are smaller than those for 1/3 by approximately a factor of 50.Comment: Accepted for PRB rapid communication (scheduled to appear in Nov 15, 2000 issue

Masses of composite fermions carrying two and four flux quanta: Differences and similarities

This study provides a theoretical rationalization for the intriguing experimental observation regarding the equality of the normalized masses of composite fermions carrying two and four flux quanta, and also demonstrates that the mass of the latter type of composite fermion has a substantial filling factor dependence in the filling factor range $4/17 > \nu > 1/5$, in agreement with experiment, originating from the relatively strong inter-composite fermion interactions here.Comment: 5 pages, 2 figure

Partially spin polarized quantum Hall effect in the filling factor range 1/3 < nu < 2/5

The residual interaction between composite fermions (CFs) can express itself through higher order fractional Hall effect. With the help of diagonalization in a truncated composite fermion basis of low-energy many-body states, we predict that quantum Hall effect with partial spin polarization is possible at several fractions between $\nu=1/3$ and $\nu=2/5$. The estimated excitation gaps are approximately two orders of magnitude smaller than the gap at $\nu=1/3$, confirming that the inter-CF interaction is extremely weak in higher CF levels.Comment: 4 pages, 3 figure

Girvin-MacDonald-Platzman Collective Mode at General Filling Factors: Magneto-Roton Minimum at Half-Filled Landau Level

The single mode approximation has proved useful for the excitation spectrum at $\nu=1/3$. We apply it to general fractions and find that it predicts $n$ magneto-roton minima in the dispersion of the Girvin-MacDonald-Platzman collective mode for the fractional quantum Hall states at $\nu=n/(2n+1)$, and one magneto-roton minimum for both the composite Fermi sea and the paired composite fermion state. Experimental relevance of the results will be considered.Comment: 5 pages, 6 figure

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

Roton Instability of the Spin Wave Excitation in the Fully Polarized Quatum Hall State and the Phase Diagram at ν=2\nu = 2

We consider the effect of interactions on electrons confined to two dimensions at Landau level filling $\nu=2$, with the specific aim to determine the range of parameters where the fully polarized state is stable. We calculate the charge and the spin density collective modes in random phase approximation (RPA) including vertex corrections (also known as time dependent Hartree Fock), and treating the Landau level mixing accurately within the subspace of a single particle hole pair. It is found that the spin wave excitation mode of the fully polarized state has a roton minimum which deepens as a result of the interaction induced Landau level mixing, and the energy of the roton vanishes at a critical Zeeman energy signaling an instability of the fully polarized state at still lower Zeeman energies. The feasibility of the experimental observation of the roton minimum in the spin wave mode and its softening will be discussed. The spin and charge density collective modes of the unpolarized state are also considered, and a phase diagram for the $\nu =2$ state as a function of $r_{S}$ and the Zeeman energy is obtained.Comment: 47 pages, 9 figure

Optical properties of a two-dimensional electron gas at even-denominator filling fractions

The optical properties of an electron gas in a magnetic field at filling fractions \nu = {1\over 2m} (m=1,2,3...) are investigated using the composite fermion picture. The response of the system to the presence of valence-band holes is calculated. The shapes of the emission spectra are found to differ qualitatively from the well-known electron-hole results at zero magnetic field. In particular, the asymmetry of the emission lineshape is found to be sensitive to the hole-composite fermion plane separation.Comment: 17 pages, LaTeX, 7 figures. This revised version is to appear in Physical Review

First demonstration of single trench fiber for delocalization of higher order modes

We demonstrate an ytterbium-doped single-trench fiber ensuring a high losses ratio (~1000) and low power fraction (~0.7) between the higher-order-modes and fundamental-mode with excellent bend robustness and 85% laser efficiency at a wavelength of 1040nm

How universal is the fractional-quantum-Hall edge Luttinger liquid?

This article reports on our microscopic investigations of the edge of the fractional quantum Hall state at filling factor $\nu=1/3$. We show that the interaction dependence of the wave function is well described in an approximation that includes mixing with higher composite-fermion Landau levels in the lowest order. We then proceed to calculate the equal time edge Green function, which provides evidence that the Luttinger exponent characterizing the decay of the Green function at long distances is interaction dependent. The relevance of this result to tunneling experiments is discussed.Comment: 5 page