Topological Structures and Corresponding Accurate Ground State Wave Functions for ν=2+½ Fractional Quantum Hall Effect

The fractional quantum Hall state at ν=2+½ remains enigmatic because of the lack of accurate ground state wave function for Coulomb interaction. It is believed that the most probable ground state wave function is one of those two associated with incompressible state occuring in spherical geometry for the Pfaffian and anti-Pfaffian flux shifts 3 and -1, given by the respective total number of flux quanta, N_Φ=2N-3 and 2N+1. Although the well known Moore-Read wave function and its particle-hole conjugate partner belong to these shifts, these most likely do not describe true topology of the Coulomb state. Starting with these flux and particle relations, we determine corresponding topological structures, i.e., number of zeros felt by an electron at the positions of other N-1 electrons. Using these, we determine all possible linearly independent antysymmetric functions in Jastrow form for small systems. A linear conbination of these antysymmetric functions represents the actual ground state wave function for Coulomb interaction . We obtain these wave functions for N=10 and 8 respectively for Pfaffian and anti-Pfaffian shifts. The character of these wave functions suggest the physics of 2+½ state is beyond the weak coupling regime of cooper pairs of composite fermions.