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

Theory of Incompressible States in a Narrow Channel

We report on the properties of a system of interacting electrons in a narrow channel in the quantum Hall effect regime. It is shown that an increase in the strength of the Coulomb interaction causes abrupt changes in the width of the charge-density profile of translationally invariant states. We derive a phase diagram which includes many of the stable odd-denominator states as well as a novel fractional quantum Hall state at lowest half-filled Landau level. The collective mode evaluated at the half-filled case is strikingly similar to that for an odd-denominator fractional quantum Hall state.Comment: 4 pages, REVTEX, and 4 .ps file

Impurity Effects and Spin Polarizations in a Narrow Quantum Hall System

The temperature dependence of electron spin polarization for a narrow quantum Hall system shows behavior analogous to that of a two-dimensional system at major filling factors. At the lowest half-filled quantum Hall state for which no two-dimensional analog exists, we find a stable spin partially-polarized system. Periodic Gaussian repulsive impurities (antidots) in such a system leads to novel spin transitions at $\nu=\frac13$ and $\nu=\frac12$ and the pair-correlation functions provide clues about nature of different ground states in the system. These results can be explored in optical spectroscopy and optically pumped NMR Knight shift measurements.Comment: 4 pages, REVTEX, and 4 .ps file