The Hierarchy of Fractional Quantum Hall States and Berry Phase

Abstract

The Hierarchy of Fractional Quantum Hall (FQH) states have been studied here in the framework of chiral anomaly and Berry Phase. It is shown that the unambiguously observed FQH states with filling factor ν=p/q with p even or odd and q an odd integer can be considered from the viewpoint that the Berry phase associated with even number of vortices can be removed to the dynamical phase and the corresponding fermionic state attains a higher Landau level. This also leads to the fact that FQH states with even denominator filling factor can arise when we have pairs of degenerate electrons giving rise to the non-Abelian Berry phase which suggests that these FQH states correspond to non-Abelian Hall fluid. In this framework Integer Quantum Hall Effect (IQHE) as well as Fractional Quantum Hall Effect (FQHE) with filling factor ν=p/q with q odd or even can be studied in a unified way.