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

Abstract

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.

arXiv comment13 pages in plain Latex

Cited by in corpus (1)

• Coexisting Vortices and Antivortices Generated by Dually Gauged Harmonic Maps