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We examine theoretically the effects caused by a periodic external potential on the correlated motion of a two-dimensional electron system under strong magnetic fields corresponding to a filling factor 1/2. To describe the resulting complex dynamics, we adopt a composite fermion approach and we determine in a two loop approximation the density-response function $K_{00}(\bfq,\omega)$ and the compressibility. We show explicitly that the long-wavelength limit of $K_{00}(\bfq,\omega)$ exhibits substantial anisotropic behavior induced by the modulation, and that the system tends to be incompressible in a direction orthogonal to the modulation as opposed to its response along the modulation., Comment: 8 pages and 1 figure

An interacting double layer system, with uniform positive background, is studied at finite temperature in the presense of a strong magnetic field corresponding to half filling in each layer. By mapping this system to composite fermions in zero field, we investigate the momentum transfer rate between the layers. As a result of the residual gauge interactions, it turns out that the low temperature dependence of this rate is $T^{4/3}$ which is enhanced as compared to the normal $T^2$ behavior., Comment: 8 pages, Phyzzx macro

The phase structure of a $(2+1)$ - dimensional model of relativistic fermions with a four fermi interaction is analyzed in the strong coupling regime using the large $N$ perturbation theory. It is shown that, this model exhibits a low temperature superconducting phase due to the vortex-anti vortex binding via Kosterlitz-Thouless mechanism. Above a critical temperature, vortices unbind and superconductivity is destroyed; at a still higher temperature the vacuum expectation value of a neutral order parameter vanishes. The ground state respects parity and time reversal symmetries., Comment: 10 pages, Revtex

The possibility of charge density oscillations in a {\it finite-thickness} two-dimensional system is investigated for strong magnetic fields and integer filling factors. Using an effective action formalism, it is shown that an {\it oscillatory charge density} (OCD) is generated in a self-consistent way and is favored energetically over homogeneous distributions. It is smooth on the scale of the sample thickness and of the magnetic length. The modulus of its wave vector is shown to be experimentally accessible. The Hall voltage and the current density are shown to {\it oscillate} with the same wave vector when a weak current is applied. The stability of the charge oscillations against impurity potentials is discussed., Comment: 12 pages, REVTeX 3.0

The effective action of nonrelativistic fermions in 2+1 dimensions is analyzed at finite temperature and chemical potential in the presence of a uniform magnetic field perpendicular to the plane. The method used is a generalization of the derivative expansion technique. The induced Chern-Simons term is computed and shown to exhibit the Hall quantization. Effects of dissipation due to collisions are also analyzed., Comment: 12 pages

We analyse a $2+1$ dimensional model with charged, relativistic fermions interacting through a four-Fermi term. Taking advantage of its large-$N$ renormalizability, the various phases of this model are studied at finite temperature and beyond the leading order in $1/N$. Although the vacuum expectation value (VEV) of a charged order parameter is zero at any non-zero temperature, the model nevertheless exhibits a rich phase structure in the strong coupling r\'egime, because of the non-vanishing VEV of a neutral order parameter and due to the non-trivial dynamics of the vortex excitations on the plane. These are: a confined-vortex phase which is superconducting at low temperatures, an intermediate-temperature phase with deconfined vortices, and a high-temperature phase, where the neutral order parameter vanishes. The manifestation of superconductivity at low-temperatures and its disappearance above a critical temperature is explicitly shown to be due to the vortex confinement/deconfinement mechanism of Kosterlitz and Thouless. The ground state does not break parity or time-reversal symmetries and the ratio of the energy gap to $T_c$ is bigger than the conventional BCS value, for $N\ltwid 22$., Comment: 27 pages + 4 figures and several diagrammatic equations, available from authors upon request, UdeM-LPN-TH-147