The nature of composite fermions and the role of particle hole symmetry: A microscopic account

Abstract

Motivated by the issue of particle-hole symmetry for the composite fermion Fermi sea at the half filled Landau level, Dam T. Son has made an intriguing proposal [Phys. Rev. X {\bf 5}, 031027 (2015)] that composite fermions are Dirac particles. We ask what features of the Dirac-composite fermion theory and its various consequences may be reconciled with the well established microscopic theory of the fractional quantum Hall effect and the 1/2 state, which is based on {\em non-relativistic} composite fermions. Starting from the microscopic theory, we derive the assertion of Son that the particle-hole transformation of electrons at filling factor $\nu =1/2$ corresponds to an effective time reversal transformation (i.e. $\{{\vec{k}}_j\}$$\to$$\{-{\vec{k}}_j\}$) for composite fermions, and discuss how this connects to the absence of $2k_{\mathrm{F}}$ backscattering in the presence of a particle-hole symmetric disorder. By considering bare holes in various composite-fermion $\Lambda$ levels (analogs of electronic Landau levels) we determine the $\Lambda$ level spacing and find it to be very nearly independent of the $\Lambda$ level index, consistent with a parabolic dispersion for the underlying composite fermions. Finally, we address the compatibility of the Chern-Simons theory with the lowest Landau level constraint, and find that the wave functions of the mean-field Chern-Simons theory, as well as a class of topologically similar wave functions, are surprisingly accurate when projected into the lowest Landau level. These considerations lead us to introduce a "normal form" for the unprojected wave functions of the $n/(2pn-1)$ states that correctly capture the topological properties even without lowest Landau level projection.

arXiv comment17 pages, 3 figures, published version

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• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Particle-hole symmetry and composite fermions in fractional quantum Hall states
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• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Lattice Monte Carlo for Quantum Hall States on a Torus
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• Quench dynamics of collective modes in fractional quantum Hall bilayers
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
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• 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
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Quantum Hall hierarchy from coupled wires
• Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
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• Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula
• Theoretical phase diagram of two-component composite fermions in double layer graphene
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• Particle-vortex symmetric liquid
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• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Geometric Resonance of Four-Flux Composite Fermions
• Why is the HLR theory particle-hole symmetric?
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• Particle-Hole Symmetry and the Reentrant Integer Quantum Hall Wigner Solid
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• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
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• Pairing instabilities of Dirac composite fermions
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
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• The composite fermion theory revisited: a microscopic derivation without Landau level projection
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• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• On dualities of paired quantum Hall bilayer states at ${\nu }_T=\frac{1}{2}+\frac{1}{2}$
• Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study
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• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
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• Emergence of Dirac Composite Fermions: Dipole Picture