Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels

TL;DR

This paper investigates phase transitions in half-filled Landau levels, identifying a first order transition to a Moore-Read paired state in higher levels and a weaker transition in the lowest level, influenced by electron layer width.

Contribution

It provides new insights into the nature of phase transitions between stripe, paired, and composite fermion liquid phases in Landau levels, highlighting the role of layer width and Coulomb potential proximity.

Findings

First order transition to Moore-Read state near Coulomb potential in higher Landau level.

Weaker pairing transition in the lowest Landau level.

Transition can be driven by changing electron layer width.

Abstract

We consider the two lowest Landau levels at half filling. In the higher Landau level (nu =5/2), we find a first order phase transition separating a compressible striped phase from a paired quantum Hall state, which is identified as the Moore-Read state. The critical point is very near the Coulomb potential and the transition can be driven by increasing the width of the electron layer. We find a much weaker transition (either second order or a crossover) from pairing to the composite fermion Fermi liquid behavior. A very similar picture is obtained for the lowest Landau level but the transition point is not near the Coulomb potential.