CHERN-SIMONS GAUGE THEORY FOR DOUBLE-LAYER ELECTRON SYSTEM

Abstract

We present a microscopic theory of the fractional quantum Hall effect at the filling factor ν with even denominator, which is recently observed in a double-layer electron system. In our approach electrons belonging to different layers are interpreted as different types of anyons with appropriate statistics. The wavefunction of the Hall state is calculated, which is found to coincide with that of Halperin. We also analyze vortex (quasihole) excitations. It is shown that a single vortex carries electric charges on both of the layers; for instance, a vortex at ν=½ has the electric charge [Formula: see text] on one layer and -⅛e on the other layer. The ground state at the vicinity of ν=½ is given by a Wigner crystal made of these vortices.