Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities
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Date
2021-09-23
Journal Title
Journal ISSN
Volume Title
Journal Title
Physical Review B
Volume Title
104
Article Title
115150
Publisher
American Physical Society (APS)
Abstract
Building on previous work [N. Read, Phys. Rev. B58, 16262 (1998)10.1103/PhysRevB.58.16262; Z. Dong and T. Senthil, Phys. Rev. B102, 205126 (2020)10.1103/PhysRevB.102.205126] on the system of bosons at filling factor , we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and apply 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 -wave pairing in the lowest Landau level, and strong coupling -wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.