Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea

Abstract

The fully spin polarized composite fermion (CF) Fermi sea at half filled lowest Landau level has a Fermi wave vector $k_{\mathrm{F}}^{\ast }=\sqrt{4\pi {\rho }_e}$, where ${\rho }_e$ is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can be treated perturbatively. Away from $\nu =1/2$, the area is seen to be consistent with $k_{\mathrm{F}}^{\ast }=\sqrt{4\pi {\rho }_e}$ for $\nu <1/2$ but $k_{\mathrm{F}}^{\ast }=\sqrt{4\pi {\rho }_h}$ for $\nu >1/2$, where ${\rho }_h$ 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 $\nu =1/2$, 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 $\nu =1/2$ are consistent with $k_{\mathrm{F}}^{\ast \uparrow ,\downarrow }=\sqrt{4\pi {\rho }_e^{\uparrow ,\downarrow }}$, where ${\rho }_e^{\uparrow }={\rho }_e^{\downarrow }={\rho }_e/2$, which implies that the residual interactions between composite fermions do not cause a non-perturbative correction for non-fully spin polarized CFFS either. Our results suggest the natural conjecture that for arbitrary spin polarization the CF Fermi wave vectors are given by $k_{\mathrm{F}}^{\ast \uparrow }=\sqrt{4\pi {\rho }_e^{\uparrow }}$ and $k_{\mathrm{F}}^{\ast \downarrow }=\sqrt{4\pi {\rho }_e^{\downarrow }}$.

12 pages, 9 figures and 2 tables (published version), updated references, corrected x-axis labels in Fig. 9 and added data for $\nu =9/19$ in Fig. 9

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