Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Abstract

Building on previous work [N. Read, Phys. Rev. B 58, Z. Dong and T. Senthil, 16262 (1998); Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor $\nu =1$, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and applying the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling $p$-wave pairing in the lowest Landau level, and strong coupling $p$-wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.

arXiv comment15 pages, 5 figures, 2 appendices, typos corrected

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• Noncommutative gauge symmetry in the fractional quantum Hall effect
• Quantum Hall bilayer in dipole representation
• Quantum mechanics of composite fermions
• PH Pfaffian intra and inter correlations in the quantum Hall bilayer
• Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study
• Fermion liquids as quantum Hall liquids in phase space: A unified approach for anomalies and responses
• Dipole representation of composite fermions in graphene quantum Hall systems
• Twisted holographic superconductors in external magnetic field
• Emergence of Dirac Composite Fermions: Dipole Picture