Fermi wave vector for the partially spin-polarized composite-fermion Fermi sea

The fully spin-polarized composite-fermion (CF) Fermi sea at the half-filled lowest Landau level has a Fermi wave vector kF∗=4πρe, where ρe is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can be treated perturbatively. Away from ν=1/2, the area is seen to be consistent with kF∗=4πρe for ν<1/2 but kF∗=4πρh for ν>1/2, where ρh is the density of holes in the lowest Landau level. This result is consistent with particle-hole symmetry in the lowest Landau level. We investigate in this article the Fermi wave vector of the spin-singlet CF Fermi sea (CFFS) at ν=1/2, for which particle-hole symmetry is not a consideration. Using the microscopic CF theory, we find that for the spin-singlet CFFS the Fermi wave vectors for up- and down-spin CFFSs at ν=1/2 are consistent with kF∗↑,↓=4πρe↑,↓, where ρe↑=ρe↓=ρe/2, which implies that the residual interactions between composite fermions do not cause a nonperturbative correction for spin-singlet CFFS either. Our results suggest the natural conjecture that for arbitrary spin polarization the CF Fermi wave vectors are given by kF∗↑=4πρe↑ and kF∗↓=4πρe↓.