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While an ordinary Fermi sea is perturbatively robust to interactions, theparadigmatic composite-fermion (CF) Fermi sea arises as a non-perturbativeconsequence of emergent gauge fields in a system where there was no Fermi seato begin with. A mean-field picture suggests two Fermi seas, of compositefermions made from electrons or holes in the lowest Landau level, which occupydifferent areas away from half filling and thus appear to represent distinctstates. We show that in the microscopic theory of composite fermions, whichsatisfies particle-hole symmetry in the lowest Landau level to an excellentdegree, the Fermi wave vectors at filling factors $\nu$ and $1-\nu$ are thesame, and are generally consistent with the experimental findings of Kamburov{\em et al.} [Phys. Rev. Lett. {\bf 113}, 196801 (2014)]. Our calculationssuggest that the area of the CF Fermi sea may slightly violate the Luttingerarea rule.

Luttinger theorem for the strongly correlated Fermi liquid of composite fermions