Fermi wave vector for the partially spin-polarized composite-fermion Fermi sea
Research output: Contribution to journal › Journal article › Research › peer-review
The fully spin polarized composite fermion (CF) Fermi sea at half filled lowest Landau level has a Fermi wave vector $k^*_{\rm F}=\sqrt{4\pi\rho_e}$, 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 $k^*_{\rm F}=\sqrt{4\pi\rho_e}$ for $\nu<1/2$ but $k^*_{\rm F}=\sqrt{4\pi\rho_h}$ 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 $k^{*\uparrow,\downarrow}_{\rm F}=\sqrt{4\pi\rho^{\uparrow,\downarrow}_e}$, where $\rho^{\uparrow}_e=\rho^{\downarrow}_e=\rho_e/2$, 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 $k^{*\uparrow}_{\rm F}=\sqrt{4\pi\rho^{\uparrow}_e}$ and $k^{*\downarrow}_{\rm F}=\sqrt{4\pi\rho^{\downarrow}_e}$.
Original language | English |
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Article number | 235102 |
Journal | Physical Review B |
Volume | 96 |
Issue number | 23 |
Number of pages | 12 |
ISSN | 2469-9950 |
DOIs | |
Publication status | Published - 1 Dec 2017 |
Bibliographical note
[Qdev]
Links
- http://arxiv.org/pdf/1707.08623
Submitted manuscript
ID: 186326339