Polarization Of Quantum Hall States, Skyrmions and Berry Phase

We have discussed here the polarization of quantum Hall states in the framework of the hierarchical analysis of IQHE and FQHE in terms of Berry phase. It is observed that we have fully polarized states for the filling factor $\nu=1$ as well as $\nu=\frac{1}{2m+1}$, $m$ being an integer. However, for $\nu=p$ as well as $\nu =\frac{p}{q}$, with $p>1$ and odd, $q$ odd we have partially polarized states and for $\nu=\frac{p}{q}$, $p$ even, $q$ odd we have unpolarized states. It has been found that skyrmion excitations exist only for fully polarized states and for partially polarized and unpolarized states skyrmionic excitations do not exist.