Paired Hall States

This dissertation contains a collection of individual articles on various topics. Their significance in the corresponding field as well as connections between them are emphasized in a general and comprehensive introduction. In the first article, we explore the consequences for macroscopic effective Lagrangians of assuming that the momentum density is proportional to the flow of conserved current. The universal corrections we obtain for the macroscopic Lagranigian of a superconductor describe the London Hall effect, and provide a fully consistent derivation of it. In the second article, we propose a heuristic principle for quantized Hall states: the existence and incompressibility of fractionally quantized Hall states is explained by an argument based on an adiabatic localization of magnetic flux, the process of trading uniform flux for an equal amount of fictitious flux attached to the particles. This principle is exactly implemented in the third article. For a certain class of model Hamiltonians, we obtain Laughlin's Jastrow type wave functions explicitly from a filled Landau level, by smooth extrapolation in quantum statistics. The generalization of this analysis to the torus geometry shows that theorems restricting the possibilities of quantum statistics on closed surfaces are circumvented in the presence of a magnetic field. In the last article, we propose the existence of a novel incompressible quantum liquid, a paired Hall state, at a half filled Landau level. This state arises adiabatically from free fermions in zero magnetic field, and reduces to a state previously proposed by Halperin in the limit of tightly bound pairs. It supports unusual excitations, including neutral fermions and charge e/4 anyons with statistical parameter theta=pi/8..