The principle that perturbation in quantum statistics should be accompanied by application of an appropriate magnetic field has been successful in giving a simple understanding of major qualitative features of the fractional quantized Hall states and related anyon superconducting states. In these applications, the starting point is one or more filled Landau levels. Here we consider the question of perturbation around free fermions. We argue that very near this point the statistical interactions are weak and their effects calculable; nevertheless they have the important qualitative consequence that a p-wave BCS pairing instability is triggered. The result is a new line of incompressible states in the (inverse) filling-fraction-statistics plane. This line extrapolates to a state obeying Fermi statistics at filling fraction 1/2, which is a candidate to describe electron states. A variety of techniques is then employed to elucidate the properties of this state and the unusual quasiparticles it supports. We believe the state is in the same universality class as one Halperin proposed based on grouping electrons into pairs of tightly bound bosonic molecules, which form a correlated state of the Laughlin type. We report the results of extensive numerical work which establishes firmly the existence of an incompressible state with the properties we predict, including the very unusual quasiparticles, for simple model potentials. We also investigate the situation for realistic potentials, and conclude that a paired Hall state of the type investigated here is a good candidate to describe real 2d electron gases, especially for thick samples and higher Landau levels, quite possibly including the state at filling fraction 5/2 that has already been observed.
