Particle-flux separation in Chern-Simons theory and the Landau-level gap of composite fermions.

Abstract

We study a system of nonrelativistic fermions in a uniform magnetic field near the half-filled Landau level (\ensuremath{\nu}\ensuremath{\simeq}1/2) from a viewpoint of gauge theory. At the exact half filling, quasiexcitations are so-called composite fermions and dynamically generated gauge bosons. A composite fermion (CF) is an electron with two flux quanta attaching to it. Because of interactions between fermions and gauge bosons, there appears anomalous behavior in the fermion propagator, i.e., vanishing of Fermi velocity. We start with this picture at half filling and follow the CF approach of Jain to the fractional quantum Hall effect near half filling. We than make use of the Chern-Simons bosonization to describe these CF's in a residual magnetic field. We calculate the effective Landau-level gap of CF, and find that it tends to vanish near half filling due to the dynamical gauge field. Our calculation naturally explains the recent experiments reporting that the excitation gap of quantum Hall states behaves anomalously near half filling, i.e., enhancement of the effective mass of quasiparticles. This phenomenon can be understood by a shielding mechanism between two kinds of fluxes and the Nambu-Goldstone mode of bosonized CF's. Throughout the calculation, we assume that there are two possible phases: in one phase, particles and fluxes are bound, while in the other phase, particles and fluxes are separated, i.e., the particle-flux separation occurs.