Pairing of particle-hole symmetric composite fermions in half-filled Landau level

Abstract

In a recent proposal of the half-filled Landau level, the composite fermions are taken to be Dirac particles and particle-hole symmetric. Cooper pairing of these composite fermions in different angular momentum channels, $\ell$, can give rise to different kinds of Pfaffian states. In addition to the well known Moore-Read Pfaffian and anti-Pfaffian states, a new putative particle-hole symmetric Pfaffian state, corresponding to the $s-$wave pairing channel, was also proposed. However, the possible underlying pairing mechanism is not clear at all. In this work we provide a specific pairing mechanism for realizing some of these Pfaffian states. We show that there can be nonzero pairing in angular momentum channels $|\ell |\ge 1$ depending on the magnitude of a coupling constant. There is a quantum phase transition from the Dirac composite fermi liquid state to Cooper pairing states in angular momentum channels $|\ell |\ge 1$ as the coupling constant is tuned across its critical point value. Surprisingly the particle-hole symmetric $\ell =0$ channel pairing turns out to be impossible irrespective of the size of the coupling constant.

8 pages and 4 figures; accepted version in Phys. Rev. B including corrections regarding triplet pairing channel. Clarity of figures improved

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Linear response of doped graphene sheets to vector potentials
• Emergent particle-hole symmetry in the half-filled Landau level
• Pairing in half-filled Landau level
• Determination of the Fermi Contour and Spin-polarization of $\nu =3/2$ Composite Fermions via Ballistic Commensurability Measurements
• Pairing instabilities of Dirac composite fermions

Cited by in corpus (8)

• Bosonization and Mirror Symmetry
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Geometric Resonance of Four-Flux Composite Fermions
• Why is the HLR theory particle-hole symmetric?
• Paired states in half-filled Landau levels
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals