Paired states in half-filled Landau levels

Abstract

We discuss monolayer and bilayer quantum Hall systems in which each layer is a half-filled Landau level (LL) system. In the mean field approximation of the Son's formalism there is a common pairing structure that underlines the possibilities for paired ground states in both systems. We argue that the particle-hole (PH) Pfaffian state in the (particle-hole symmetric) half-filled LL of a monolayer, and analogous state in the PH symmetric bilayer (in which each layer is half-filled LL) can be considered as {\em critical states} i.e. states that cannot describe a phase under PH symmetry. We point out that the inclusion of a PH symmetry breaking (like LL mixing) may stabilize the PH Pfaffian in a monolayer. In the bilayer case, in numerical experiments on a sphere, by choosing the PH symmetric shift, we can stabilize the interlayer correlated (111) excitonic state or critical state, for any distance between the layers, but in general, with no bias, the evolution of the bilayer includes other phases.

9 pages, rewritten, published version with important conclusions

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• Composite fermion duality for half-filled multicomponent Landau Levels
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• The Dirac composite fermion of the fractional quantum Hall effect
• Quantum disordering of the 111 state and the compressible-incompressible transition in quantum Hall bilayer systems

Cited by in corpus (11)

• Observation of half-integer thermal Hall conductance
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Disorder-driven transition and intermediate phase for $\nu =5/2$ fractional quantum Hall effect
• Numerical Study of Quantum Hall Bilayers at Total Filling ${\nu }_T=1$: A New Phase at Intermediate Layer Distances
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Quantum Hall bilayer in dipole representation
• Topological pairing of composite fermions via criticality