Pairing instabilities of Dirac composite fermions

TL;DR

This paper explores the implications of a Dirac composite fermion framework for pairing instabilities in quantum Hall systems, revealing potential anisotropic states and transitions to Pfaffian states, with results consistent with numerical studies.

Contribution

It introduces a Dirac formalism for composite fermions and analyzes its effects on pairing, anisotropy, and phase transitions in quantum Hall systems, extending previous models.

Findings

Anisotropic states may coexist with isotropic pairings in half-filled single layers.

Anisotropic pairings with PH symmetry breaking can evolve into Pfaffian states.

Weak p-wave pairing in bilayers transitions from Dirac to HLR-like composite fermions.

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.