Luttinger theorem for the strongly correlated Fermi liquid of composite fermions

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.

21 pages, 17 figures including supplemental material, published version

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Cited by in corpus (52)

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• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Emergent particle-hole symmetry in the half-filled Landau level
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect
• Particle-Hole Duality in the Lowest Landau Level
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• Composite Fermions on a Torus
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Composite fermion pairing induced by Landau level mixing
• Weiss oscillations and particle-hole symmetry at the half-filled Landau level
• Berry Phase and Anomalous Transport of the Composite Fermions at the Half-Filled Landau Level
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Geometric Resonance of Four-Flux Composite Fermions
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Fluctuations and magnetoresistance oscillations near the half-filled Landau level
• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
• Pairing of particle-hole symmetric composite fermions in half-filled Landau level
• Cyclotron Orbits of Composite Fermions in the Fractional Quantum Hall Regime
• Emergent reflection symmetry from non-relativistic composite fermions
• Parametrization and thermodynamic scaling of pair correlation functions for the Fractional Quantum Hall Effect
• Pairing instabilities of Dirac composite fermions
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Weiss Oscillations in the Galilean-Invariant Dirac Composite Fermion Theory for Even-Denominator Filling Fractions of the Lowest Landau Level
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
• Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study
• Nonperturbative emergence of Dirac fermion in strongly correlated composite fermions of fractional quantum Hall effects
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases