The edge of spin-unpolarized or spin-polarized ν=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 an 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 counterpropagating 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 one-dimensional Tomonaga-Luttinger liquids, with the spin and charge modes moving in opposite directions.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Sep 20 2012|
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics