Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States

TL;DR

This paper investigates the phase diagram of half-filled bilayer systems in the second Landau level, predicting two distinct quantum Hall states—Abelian and non-Abelian—based on tunneling and layer separation, with implications for non-Abelian state detection.

Contribution

It predicts the existence of two distinct fractional quantum Hall states in bilayer systems, linking their occurrence to tunneling and layer separation parameters, and highlights a quantum phase transition between them.

Findings

Two FQHE branches: Abelian 331 state and non-Abelian Pfaffian state.

Phase transition between the two states as tunneling and separation vary.

Experimental signatures could confirm non-Abelian state presence.

Abstract

The quantum Hall phase diagram of the half-filled bilayer system in the second Landau level is studied as a function of tunneling and layer separation using exact diagonalization. We make the striking prediction that bilayer structures would manifest two distinct branches of incompressible fractional quantum Hall effect (FQHE) corresponding to the Abelian 331 state (at moderate to low tunneling and large layer separation) and the non-Abelian Pfaffian state (at large tunneling and small layer separation). The observation of these two FQHE branches and the quantum phase transition between them will be compelling evidence supporting the existence of the non-Abelian Pfaffian state in the second Landau level.