Abstract:
We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of abelian and nonabelian quantum Hall states. While path dependent geometric phases can perturb the abelian part of the statistics, we find that the nonabelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.

Abstract:
The Fermionic Chern-Simons approach has had remarkable success in the description of quantum Hall states at even denominator filling fractions $\nu=\frac{1}{2m}$. In this paper we review a number of recent works concerned with modeling this state as a Landau-Silin Fermi liquid. We will then focus on one particular problem with constructing such a Landau theory that becomes apparent in the limit of high magnetic field, or equivalently the limit of small electron band mass $m_b$. In this limit, the static response of electrons to a spatially varying magnetic field is largely determined by kinetic energy considerations. We then remedy this problem by attaching an orbital magnetization to each fermion to separate the current into magnetization and transport contributions, associated with the cyclotron and guiding center motions respectively. This leads us to a description of the $\nu=\frac{1}{2m}$ state as a Fermi liquid of magnetized composite fermions which correctly predicts the $m_b$ dependence of the static and dynamic response in the limit $m_b \rightarrow 0$. As an aside, we derive a sum rule for the Fermi liquid coefficients for the Chern-Simons Fermi liquid. This paper is intended to be readable by people who may not be completely familiar with this field.

Abstract:
When a surface acoustic wave (SAW) is coupled piezoelectrically to a two dimensional electron gas (2DEG), a velocity shift and attenuation of the SAW are induced that reflect the conductivity of the 2DEG. This paper considers the case of a AlGaAs heterostructure with a 2DEG a distance $d$ from a (100) surface of the crystal where the SAWs are propagated in the [011] direction at wavevector $q$. It is found that the velocity shift $\Delta v_s$ and the attenuation coefficient $\kappa$ satisfy the well known equation $(\Delta v_s/v_s) - (i \kappa/q) = (\alpha^2/2)/\left(1 + \frac{i \sigma_{xx}(q,\omega)} {\sigma_m}\right)$ where $\sigma_{xx}(q,\omega)$ is the complex conductivity at wavevector $q$ and frequency $\omega = v_s q$ with $v_s$ the velocity of the SAW. The coefficients $\alpha$ and $\sigma_m$ are calculated and it is found that $\alpha$ has a nontrivial dependence on the product $qd$.

Abstract:
We give an explicit expression for the M-point correlator of the superconformal current in two dimensional N=1 superconformal field theories.

Abstract:
A device is proposed that is similar in spirit to the electron turnstile except that it operates within a quantum Hall fluid. In the integer quantum Hall regime, this device pumps an integer number of electrons per cycle. In the fractional regime, it pumps an integer number of fractionally charged quasiparticles per cycle. It is proposed that such a device can make an accurate measurement of the charge of the quantum Hall effect quasiparticles.

Abstract:
The composite fermion picture has had a remarkable number of recent successes both in the description of the fractional quantized Hall states and in the description on the even denominator Fermi liquid like states. In this review we give an introductory account of the Chern-Simons fermion theory, focusing on the description of the even denominator states as unusual Fermi liquids. Contents include: 1. Introduction 2. Introduction to Chern-Simons Fermions 3. RPA 4. Landau Fermi Liquid Theory and MRPA 5. Magnetization and M2RPA 6. Perturbative Approaches and Trouble in the Infrared 7. Wavefunction Picture of Composite Fermions and Dipole Approach 8. Selected Experiments 9. Last Words

Abstract:
In a recent letter M. Lilly et al [PRL 82, 394 (1999)] have shown that a highly anisotropic state can arise in certain two dimensional electron systems. In the large square samples studied, resistances measured in the two perpendicular directions are found to have a ratio that may be 60 or larger at low temperature and at certain magnetic fields. In Hall bar measurements, the anisotropy ratio is found to be much smaller (roughly 5). In this comment we resolve this discrepancy by noting that the anisotropy of the underlying sheet resistivities is correctly represented by Hall bar resistance measurements but shows up exponentially enhanced in resistance measurements on square samples due to simple geometric effects. We note, however, that the origin of this underlying resistivity anisotropy remains unknown, and is not addressed here.

Abstract:
This tutorial paper reviews some of the physics of quantum Hall bilayers with a focus on the case where there is low or zero tunnelling between the two layers. We describe the interlayer coherent states at filling factors nu=1 and nu=2 as exciton condensates and discuss some of the theory associated with these states.

Abstract:
In this paper we study fractional quantum Hall composite fermion wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these filling fractions, there are several possible wavefunctions with different spin polarizations, depending on how many spin-up or spin-down composite fermion Landau levels are occupied. We calculate the energy of the possible composite fermion wavefunctions and we predict transitions between ground states of different spin polarizations as the ratio of Zeeman energy to Coulomb energy is varied. Previously, several experiments have observed such transitions between states of differing spin polarization and we make direct comparison of our predictions to these experiments. For more detailed comparison between theory and experiment, we also include finite-thickness effects in our calculations. We find reasonable qualitative agreement between the experiments and composite fermion theory. Finally, we consider composite fermion states at filling factors \nu = 2+2/3, 2+3/5, and 2+4/7. The latter two cases we predict to be spin polarized even at zero Zeeman energy.