Pfaffian and fragmented states at nu=5/2 in quantum Hall droplets

Abstract

When a gas of electrons is confined to two dimensions, application of a strong magnetic field may lead to startling phenomena such as emergence of electron pairing. According to a theory this manifests itself as appearance of the fractional quantum Hall effect with a quantized conductivity at an unusual half-integer nu=5/2 Landau level filling. Here we show that similar electron pairing may occur in quantum dots where the gas of electrons is trapped by external electric potentials into small quantum Hall droplets. However, we also find theoretical and experimental evidence that, depending on the shape of the external potential, the paired electron state can break down, which leads to a fragmentation of charge and spin densities into incompressible domains. The fragmentation of the quantum Hall states could be an issue in the proposed experiments that aim to probe for non-abelian quasi-particle characteristics of the nu=5/2 quantum Hall state.

arXiv comment9 pages, 8 figures

References in corpus (26)

• Non-Abelian Anyons and Topological Quantum Computation
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Correlation energy and spin polarization in the 2D electron gas
• The Addition Spectrum of a Lateral Dot from Coulomb and Spin Blockade Spectroscopy
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Subsurface charge accumulation imaging of a quantum Hall liquid
• Spin-density-functional theory of circular and elliptical quantum dots
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Three real-space discretization techniques in electronic structure calculations
• Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
• Paired composite fermion wavefunctions
• Detecting non-Abelian Statistics with Electronic Mach-Zehnder Interferometer
• Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories
• Broken Symmetry in Density-Functional Theory: Analysis and Cure
• Density functional theory of the phase diagram of maximum density droplets in two-dimensional quantum dots in a magnetic field
• Spin-droplets in confined quantum Hall systems
• Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields
• Half-Integer Filling Factor States in Quantum Dots
• Variational Monte Carlo for Interacting Electrons in Quantum Dots
• Interacting electrons on a quantum ring: exact and variational approach
• Multiple transitions of the spin configuration in quantum dots
• Probing a Kondo correlated quantum dot with spin spectroscopy

Cited by in corpus (10)

• Vortices in quantum droplets: Analogies between boson and fermion systems
• Transport properties of quantum dots in the Wigner molecule regime
• Interaction-Induced Spin Polarization in Quantum Dots
• Reduced density-matrix functional theory in quantum Hall systems
• Semi-local density functional for the exchange-correlation energy of electrons in two dimensions
• Effects of thickness in quantum dots at strong magnetic fields
• Quantum Hall droplet laterally coupled to a quantum ring
• Formation of spin droplet at nu = 5/2 in an asymmetric quantum dot under quantum Hall conditions
• Stability of spin droplets in realistic quantum Hall devices
• Optimal confinement potential in quantum Hall droplets