Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement

Abstract

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $\nu =5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge $+e/4$ quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.

4 pages, 3 figures. New version shortened for PRL. Corrected typos

References in corpus (3)

• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State
• Edge excitations and Topological orders in rotating Bose gases

Cited by in corpus (23)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Anyons and the quantum Hall effect - a pedagogical review
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Thermopower as a Possible Probe of Non-Abelian Quasiparticle Statistics in Fractional Quantum Hall Liquids
• Experimental probe of topological orders and edge excitations in the second Landau level
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Edge States and Interferometers in the Pfaffian and anti-Pfaffian States
• Observable Bulk Signatures of Non-Abelian Quantum Hall States
• Thermopower of Quantum Hall States in Corbino Geometry as a Measure of Quasiparticle Entropy
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Trapping Abelian anyons in fractional quantum Hall droplets
• Probing the $\nu =\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States
• Landscapes of an out-of-equilibrium anyonic sea
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids