Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect

Abstract

The edge of spin unpolarized or spin polarized $\nu =2/3$ fractional quantum Hall states is predicted by the effective theory to support a backward moving neutral mode in addition to a forward moving charge mode. We study this issue from a microscopic perspective where these states are identified with effective filling factor of 2 of composite fermions, but with an effective magnetic field that is antiparallel to the external field. A simple counting from the composite fermion description suggests that there might be two backward moving edge modes, but explicit calculations show that one of these is projected out of the low energy sector, while the remaining mode provides a good microscopic account of the actual counter propagating edge mode. The forward moving modes are identified as "Schur modes," obtained by multiplying the ground state wave function by the symmetric Schur polynomials. The edge of the 2/3 spin unpolarized state provides a particularly striking realization of "spin charge separation" in a one dimensional Tomonaga Luttinger liquids, with the spin and charge modes moving in opposite directions.

References in corpus (30)

• Topological orders and Edge excitations in FQH states
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Fractional Quantum Hall States and Jack Polynomials
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Observation of neutral modes in the fractional quantum Hall regime
• Band Structure of the Fractional Quantum Hall Effect
• Reconstruction of Fractional Quantum Hall Edges
• Edge reconstruction in the fractional quantum Hall regime
• Composite Fermions in Quantum Dots
• Tunneling into the edge of a compressible Quantum Hall state
• Spinful Composite Fermions in a Negative Effective Field
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• How universal is the fractional-quantum-Hall edge Luttinger liquid?
• Numerical Tests of the Chiral Luttinger Liquid Theory for Fractional Hall Edges
• Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid
• Effective action of a compressible QH state edge: application to tunneling
• Topological Phase Transition in the $\nu =2/3$ Quantum Hall Effect
• Excitation Spectrum and Collective Modes of Composite Fermions
• Edge reconstructions in fractional quantum Hall systems
• Testing the topological nature of the fractional quantum Hall edge
• Fractional-quantum-Hall edge electrons and Fermi statistics
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• Edge Excitations of the $\nu =2/3$ Spin-Singlet Quantum Hall State
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Semiconductor quantum dots in high magnetic fields: The composite-fermion view
• Effective field theory for the bulk and edge states of quantum Hall states in unpolarized single layer and bilayer systems
• Electronic Spectral Functions for Quantum Hall Edge States
• Microscopic study of the 2/5 fractional quantum Hall edge

Cited by in corpus (18)

• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Quantum Hall Effect of Two-Component Bosons at Fractional and Integral Fillings
• Counter-propagating charge transport in the quantum Hall effect regime
• Quantum Hall phases of two-component bosons
• Two-component quantum Hall effects in topological flat bands
• Parafermion supporting platform based on spin transitions in the fractional quantum Hall effect regime
• Non-equilibrium noise in transport across a tunneling contact between $\nu =2/3$ fractional quantum Hall edges
• Light-induced fractional quantum Hall phases in graphene
• Half-integer conductance plateau at the $\nu =2/3$ fractional quantum Hall state in a quantum point contact
• Transport in helical Luttinger liquids in the fractional quantum Hall regime
• Non-equilibrium fractional quantum Hall states visualized by optically detected MRI
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Transmission of heat modes across a potential barrier
• Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions
• Edge spin excitations and reconstructions of integer quantum Hall liquids
• Edge reconstruction of fractional quantum Hall liquids with spin degrees of freedom
• Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
• Edge reconstruction of compressible Quantum Hall fluid in the filling fraction range 1/3 to 2/3