Effective Hamiltonian for striped and paired states at the half-filled Landau level

We study a pairing mechanism for the quantum Hall system using a mean field theory with a basis on the von Neumann lattice, on which the magnetic tran slations commute. In the Hartree-Fock-Bogoliubov approximation, we solve th e gap equation Tor spin-polarized electrons at the half-filled Landau level s. We obtain an effective Hamiltonian which shows a continuous transition f rom the compressible striped state to the paired state. Furthermore, a cros sover occurs in the pairing phase. The energy spectrum and energy gap of th e quasiparticle in the paired state is calculated numerically at the half-f illed second Landau level. (C) 2001 Elsevier Science B.V. All rights reserv ed.