FRACTIONAL QUANTUM HALL EFFECT

Landau levels, filling fractions ν = p/q, anyonic excitations, Laughlin wavefunction
FQHE (1982)

Filling fraction: ν = nh/(eB)

IQHE: ν = 1,2,3,... (non-interacting)
FQHE: ν = 1/3, 2/5, 3/7,... (interactions!)

Laughlin state (1983, Nobel 1998):
Ψ = ∏ᵢ<ⱼ(zᵢ-zⱼ)^m · exp(-Σ|z|²/4l²)
m odd → fermionic, m=3 for ν=1/3

Excitations: charge e/m, statistics θ=π/m (anyons!)

ν = —
Landau level: —