Pairing instabilities of Dirac composite fermions

Abstract

Recently, a Dirac (particle-hole symmetric) description of composite fermions\nin the half-filled quantum Hall system was proposed [D. T. Son, Phys. Rev. X 5,\n031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing\nof composite fermions (CF's). One of the main consequences is the existence of\nanisotropic states in single and bilayer systems, which was previously\nsuggested in Ref. [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015)]. We\nargue that in the half-filled single layer the gapped states may sustain\nanisotropy, because isotropic pairings may coexist with anisotropic ones.\nFurthermore, anisotropic pairings with addition of a particle-hole (PH)\nsymmetry breaking mass term may evolve into rotationally symmetric states, i.e.\nPfaffian states of Halperin-Lee-Read (HLR) ordinary CF's. On the basis of the\nDirac formalism, we argue that in the quantum Hall bilayer at total filling\none, with decreasing distance between layers weak pairing of p-wave paired CF's\nis gradually transformed from Dirac to ordinary, HLR-like, with concomitant\ndecrease in the CF number. Global characterization of low-energy spectrum based\non the Dirac CF's agrees well with previous calculations performed by exact\ndiagonalization on a torus. Finally, we discuss features of Dirac formalism\nwhen applied in this context.\n