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

TL;DR

This paper proposes a specific pairing mechanism for Dirac composite fermions in half-filled Landau levels, revealing quantum phase transitions and the conditions for various Pfaffian states, including a new particle-hole symmetric state.

Contribution

It introduces a concrete pairing mechanism for Dirac composite fermions, explaining the emergence of different Pfaffian states and the conditions for their realization.

Findings

Nonzero pairing in angular momentum channels |||  depending on coupling strength.

Quantum phase transition from Dirac composite Fermi liquid to paired states as coupling varies.

Particle-hole symmetric =0 pairing is impossible regardless of coupling size.

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.