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 (9)

• Fractional Quantum Hall States and Jack Polynomials
• Observation of neutral modes in the fractional quantum Hall regime
• 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
• Testing the topological nature of the fractional quantum Hall edge
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• 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