The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

TL;DR

This paper studies the weakly coupled Pfaffian quantum Hall state, revealing that it behaves like a Type I superconductor with vortex attraction and phase separation, contrasting with the strongly coupled case.

Contribution

It introduces the concept of a Type I quantum Hall liquid in the weak-coupling limit, highlighting the dichotomy between Type I and Type II quantum Hall phases.

Findings

Weak pairing leads to vortex attraction and phase separation.

Weakly coupled Pfaffian exhibits Type I superconductor-like behavior.

Contrast with strongly coupled Pfaffian as a Type II phase.

Abstract

The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at \nu=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.