Composite Fermion Pairing in Bilayer Quantum Hall Systems

TL;DR

This paper derives an effective Hamiltonian for composite fermions in bilayer quantum Hall systems, revealing a triplet p-wave pairing ground state and evolution of states with tunneling at specific filling factors.

Contribution

It introduces a new effective Hamiltonian for composite fermions in bilayer systems and characterizes their pairing states under various conditions.

Findings

Ground state is triplet p-wave BCS pairing of composite fermions.

At ν=1/2, the state transitions from Halperin (3,3,1) to Pfaffian with tunneling.

At ν=1, the pairing state is independent of tunneling amplitude.

Abstract

We derive the effective Hamiltonian for the composite fermion in double-layer quantum Hall systems with inter-layer tunneling at total Landau-level filling factor $\nu=1/m$, where $m$ is an integer. We find that the ground state is the triplet p-wave BCS pairing state of the composite fermions. At $\nu=1/2$, the ground state of the system evolves from the Halperin $(3,3,1)$-state toward the Pfaffian-state with increasing the tunneling amplitude. On the other hand, at $\nu=1$, the pairing state is uniquely determined independent of tunneling amplitude.