Paired and Stripe States in the Quantum Hall System

In recent experiments, highly anisotropic states are observed in the half-filled third and higher Landau levels[1]. In the half-filled second Landau level the fractional quantum Hall effect (FQHE)[2] and transition to the highly anisotropic state are observed[3]. Theoretically the anisotropic states are regarded as stripe states[4] or unidirectional charge density wave states which are plausible in the Hartree-Fock approximation and numerical calculation of small systems[5, 6]. On the other hand, the FQHE state at the half-filled second Landau level is regarded as a paired state like a superconducting state[7, 8, 9, 10]. However the microscopic mechanism of the pairing is not understood yet. How is the paired state formed by the Coulomb interaction effect? Naively it seems that there is no possibility of formation of the paired state by the repulsive force in the mean field theory.