Application of Fermi hypernetted-chain theory to spin-polarized higher-order fractional quantum Hall states

Abstract

We apply Fermi hypernetted-chain theory to study the spin polarization of higher-order fractional quantum Hall (FQH) states at filling factors in between the primary FQH sequences, $\ensuremath{\nu}=p/({q}_{e}p\ifmmode\pm\else\textpm\fi{}1)$, where ${q}_{e}$ is an even integer and $p$ is a nonzero integer. The filling factors related to the higher-order FQH states include $\ensuremath{\nu}=3/8$, $4/11$, $5/13$, $5/17$, $4/13$, $6/17$, $7/11$, and so on. We use a model of strongly interacting fermions with different spin degrees of freedom to explain the states beyond primary FQH sequences. We calculate the correlation energy, the radial distribution function, as well as the static structure function associated with the Halperin wave function adopted for the mixture states of fermions with different spins. The results are comparable with those from the residual interaction between composite fermions.