Teo-Kane wires: gap opening, chirality, and fractional Hall conductance
1/3
Filling ν
e²/3h
σ_xy
--
Bulk gap Δ/v_F
e/3
Quasi-charge
Each wire is a 1D Luttinger liquid with left/right movers φ_{R/L,n}. At filling ν=1/3, coupling g cos(φ_{R,n} − φ_{L,n+1} − 3k_F a) gaps all bulk modes while leaving unpaired chiral edge modes. The many-body gap scales as Δ ~ g^{1/(2-K)} where K is the Luttinger parameter. The resulting state has Hall conductance σ_xy = e²/(3h) and Laughlin quasiparticles with fractional charge e/3 and statistics θ = π/3.