Vortices and hierarchy of states in double-layer fractional Hall effect

Vortex solutions in $U(1)\times U(1)$ Chern-Simons theory coupled to a pair of hard-core bosons representing two layers of electrons are analysed. It is shown that there is such a range of parameters $(\alpha\beta<\gamma^{2})$ in which finite charge $(1,0)$ or $(0,1)$ vortices can not exist. Instead the minimal flux quanta are $(1,1)$ hybrids. Their statistical dominance is shown to have an influence on Haldane-Halderin hierarchy of states. The form of Coulomb potential and its influence on the range of physically acceptable states is discussed.