DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 quasiparticles themselves emerge from the strong interaction, namely, for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs’ Fermi wave vector 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 minority carriers in the lowest Landau level. Our data in this work 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.

Authors:
ORCiD logo [1];  [1];  [1];  [1];  [1];  [1];  [1];  [1]; ORCiD logo [1]
  1. Princeton Univ., NJ (United States)
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES); Gordon and Betty Moore Foundation
OSTI Identifier:
1800001
Grant/Contract Number:  
FG02-00ER45841; DMR 1709076; ECCS 1906253; MRSEC DMR 1420541; GBMF9615; GBMF5305
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 125; Journal Issue: 4; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Physics

Citation Formats

Hossain, Md. Shafayat, Mueed, M. A., Ma, M. K., Villegas Rosales, K. A., Chung, Y. J., Pfeiffer, L. N., West, K. W., Baldwin, K. W., and Shayegan, M. Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System. United States: N. p., 2020. Web. doi:10.1103/physrevlett.125.046601.
Hossain, Md. Shafayat, Mueed, M. A., Ma, M. K., Villegas Rosales, K. A., Chung, Y. J., Pfeiffer, L. N., West, K. W., Baldwin, K. W., & Shayegan, M. Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System. United States. https://doi.org/10.1103/physrevlett.125.046601
Hossain, Md. Shafayat, Mueed, M. A., Ma, M. K., Villegas Rosales, K. A., Chung, Y. J., Pfeiffer, L. N., West, K. W., Baldwin, K. W., and Shayegan, M. Mon . "Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System". United States. https://doi.org/10.1103/physrevlett.125.046601. https://www.osti.gov/servlets/purl/1800001.
@article{osti_1800001,
title = {Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System},
author = {Hossain, Md. Shafayat and Mueed, M. A. and Ma, M. K. and Villegas Rosales, K. A. and Chung, Y. J. and Pfeiffer, L. N. and West, K. W. and Baldwin, K. W. and Shayegan, M.},
abstractNote = {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 quasiparticles themselves emerge from the strong interaction, namely, for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs’ Fermi wave vector 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 minority carriers in the lowest Landau level. Our data in this work 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.},
doi = {10.1103/physrevlett.125.046601},
journal = {Physical Review Letters},
number = 4,
volume = 125,
place = {United States},
year = {Mon Jul 20 00:00:00 EDT 2020},
month = {Mon Jul 20 00:00:00 EDT 2020}
}

Works referenced in this record:

Topological order, emergent gauge fields, and Fermi surface reconstruction
journal, November 2018


Topological interpretation of the Luttinger theorem
journal, August 2017


Is the Composite Fermion a Dirac Particle?
journal, September 2015


Experimental demonstration of a Fermi surface at one-half filling of the lowest Landau level
journal, December 1993


What Determines the Fermi Wave Vector of Composite Fermions?
journal, November 2014


Divalent EuRh2Si2 as a reference for the Luttinger theorem and antiferromagnetism in trivalent heavy-fermion YbRh2Si2
journal, February 2019


Fermi Surface and Quasiparticle Excitations of Overdoped Tl 2 Ba 2 CuO 6 + δ
journal, August 2005


The Dirac Composite Fermion of the Fractional Quantum Hall Effect
journal, March 2018


Surprising robustness of particle-hole symmetry for composite-fermion liquids
journal, September 2017


Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions
journal, August 1960


The half-filled Landau level: The case for Dirac composite fermions
journal, April 2016


Positive Magnetoresistance of Composite Fermion Systems with a Weak One-Dimensional Density Modulation
journal, September 1999


Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry
journal, August 2016


Fluctuations and magnetoresistance oscillations near the half-filled Landau level
journal, October 2019


Necessary and sufficient conditions for the validity of Luttinger’s theorem
journal, June 2020


Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions
journal, October 2015


Composite Fermions
book, January 2007


Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
journal, May 2007

  • Doiron-Leyraud, Nicolas; Proust, Cyril; LeBoeuf, David
  • Nature, Vol. 447, Issue 7144
  • DOI: 10.1038/nature05872

Dirac composite fermions and emergent reflection symmetry about even-denominator filling fractions
journal, October 2018


Mirror symmetry and the half-filled Landau level
journal, December 2015


Direct Observation of Composite Fermions and Their Fully-Spin-Polarized Fermi Sea near ν = 5 / 2
journal, June 2018


Theory of the half-filled Landau level
journal, March 1993


Weiss oscillations and particle-hole symmetry at the half-filled Landau level
journal, June 2017


Pairing of particle-hole symmetric composite fermions in half-filled Landau level
journal, October 2016


How real are composite fermions?
journal, December 1993


Commensurate Composite Fermions in Weak Periodic Electrostatic Potentials: Direct Evidence of a Periodic Effective Magnetic Field
journal, September 1999


Emergent particle-hole symmetry in the half-filled Landau level
journal, August 2016


Reorientation of the Stripe Phase of 2D Electrons by a Minute Density Modulation
journal, August 2016


Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing
journal, September 2018


Particle-hole symmetry and the composite Fermi liquid
journal, October 2015

  • Barkeshli, Maissam; Mulligan, Michael; Fisher, Matthew P. A.
  • Physical Review B, Vol. 92, Issue 16
  • DOI: 10.1103/PhysRevB.92.165125

Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989


Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
journal, September 2016


Geometric Resonance of Composite Fermion Cyclotron Orbits with a Fictitious Magnetic Field Modulation
journal, September 1999


Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
journal, December 2017


Berry phase and anomalous transport of the composite fermions at the half-filled Landau level
journal, August 2017

  • Pan, W.; Kang, W.; Baldwin, K. W.
  • Nature Physics, Vol. 13, Issue 12
  • DOI: 10.1038/nphys4231

Berry Phase and Model Wave Function in the Half-Filled Landau Level
journal, October 2018


Magnetic-Field Dependence of the YbRh 2 Si 2 Fermi Surface
journal, December 2008


A coherent three-dimensional Fermi surface in a high-transition-temperature superconductor
journal, October 2003

  • Hussey, N. E.; Abdel-Jawad, M.; Carrington, A.
  • Nature, Vol. 425, Issue 6960
  • DOI: 10.1038/nature01981

Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
journal, August 2017


Nature of composite fermions and the role of particle-hole symmetry: A microscopic account
journal, June 2016