Pairing instabilities of Dirac composite fermions
arXiv:1606.03919 · doi:10.1103/PhysRevB.94.115304
Abstract
Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled quantum Hall system was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing of composite fermions (CF's). One of the main consequences is the existence of anisotropic states in single and bilayer systems, which was previously suggested in Ref. [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015)]. We argue that in the half-filled single layer the gapped states may sustain anisotropy, because isotropic pairings may coexist with anisotropic ones. Furthermore, anisotropic pairings with addition of a particle-hole (PH) symmetry breaking mass term may evolve into rotationally symmetric states, i.e. Pfaffian states of Halperin-Lee-Read (HLR) ordinary CF's. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling one, with decreasing distance between layers weak pairing of p-wave paired CF's is gradually transformed from Dirac to ordinary, HLR-like, with concomitant decrease in the CF number. Global characterization of low-energy spectrum based on the Dirac CF's agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of Dirac formalism when applied in this context.
8 pages, no figures, published version
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Cited by in corpus (6)
- Bosonization and Mirror Symmetry
- Composite fermion duality for half-filled multicomponent Landau Levels
- Why is the HLR theory particle-hole symmetric?
- Paired states in half-filled Landau levels
- A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
- Pairing of particle-hole symmetric composite fermions in half-filled Landau level