Dual vortex theory of strongly interacting electrons: A non-Fermi liquid with a twist

Abstract

As discovered in the quantum Hall effect, a very effective way for strongly repulsive electrons to minimize their potential energy is to aquire nonzero relative angular momentum. We pursue this mechanism for interacting two-dimensional electrons in zero magnetic field, by employing a representation of the electrons as composite bosons interacting with a Chern-Simons gauge field. This enables us to construct a dual description in which the fundamental constituents are vortices in the auxiliary boson fields. The resulting formalism embraces a cornucopia of possible phases. Remarkably, superconductivity is a generic feature, while the Fermi liquid is not. We identify a dual $Z_2$ symmetry which, when broken (unbroken), leads to spin-charge confinement (separation). Many aspects of our earlier discussions of the nodal liquid find surprising incarnations in this new framework.