Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors $\nu$ and $1-\nu$ are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.

Figure 1

(a) Pair-correlation function $g(r)$ as a function of $r/\ell$, where $r$ is the arc distance on the sphere. The projected wave functions in Eq. (8) have been used for its evaluation. The solid lines are fits using Eq. (1) for the initial oscillations. For clarity, the curves (except for $5/11$) have been shifted up or down by multiples of 0.02. (b) The calculated thermodynamic values of $k_F^{*}\ell$ as a function of $\nu$. The mean-field values $\sqrt{2\nu }$ and $\sqrt{2(1-\nu )}$ are also shown for reference.

Figure 2

The same as in Fig. 1 but for the unprojected wave functions ${\mathrm{\Psi }}_{n/(2n\pm 1)}^{\mathrm{un}}$. Also shown for reference is $k_F^{*\mathrm{MF}}\ell =\sqrt{2\nu }$ corresponding to the Chern-Simons mean-field theory for ${}^e\mathrm{CF}\mathrm{s}$.