Luttinger theorem for the strongly correlated Fermi liquid of composite fermions

TL;DR

This paper investigates the Fermi surface properties of composite fermions in the fractional quantum Hall regime, showing that particle-hole symmetry enforces equal Fermi wave vectors at conjugate filling factors and suggesting slight violations of the Luttinger rule.

Contribution

It demonstrates that in a microscopic, particle-hole symmetric theory, composite fermion Fermi wave vectors are equal at conjugate fillings, refining understanding of Fermi sea areas in these systems.

Findings

Fermi wave vectors at filling factors ν and 1−ν are equal.

Results are consistent with experimental observations.

The CF Fermi sea area may slightly violate the Luttinger rule.

Abstract

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a non-perturbative 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. We show that in the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent degree, the Fermi wave vectors at filling factors $\nu$ and $1-\nu$ are the same, and are generally consistent with the experimental findings of Kamburov {\em et al.} [Phys. Rev. Lett. {\bf 113}, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.