Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System

Abstract

A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger postulated that the area enclosed by the Fermi surface should remain unaffected even when electron-electron interaction is turned on, so long as the interaction does not cause a phase transition. Understanding what determines the Fermi surface size is a crucial and yet unsolved problem in strongly interacting systems such as high-$T_c$ superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasi-particles themselves emerge from the strong interaction, namely for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs' Fermi wavevector down to very low electron densities, we show that the Luttinger theorem is obeyed over a significant range of interaction strengths, in the sense that the Fermi sea area is determined by the density of the \textit{minority carriers} in the lowest Landau level. Our data also address the ongoing debates on whether or not CFs obey particle-hole symmetry, and if they are Dirac particles. We find that particle-hole symmetry is obeyed, but the measured Fermi sea area differs quantitatively from that predicted by the Dirac model for CFs.

arXiv comment6 pages, 4 figures

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Cited by in corpus (9)

• $s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $\nu =1$
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Particle-Hole Symmetry and the Reentrant Integer Quantum Hall Wigner Solid
• High spatial resolution charge sensing of quantum Hall states
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Composite Fermion Mass
• Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study
• Weiss Oscillations in the Galilean-Invariant Dirac Composite Fermion Theory for Even-Denominator Filling Fractions of the Lowest Landau Level
• Fixed-phase diffusion Monte Carlo study of the activation gap and the skyrmion excitation of $\nu =1$ system in the presence of charged impurities