Laughlin Quasihole — Fractional Quantum Hall Effect

The Laughlin wavefunction (1983) describes the ν=1/m FQHE ground state. Inserting a flux quantum creates a quasihole with fractional charge e* = e/m. Visualized as the probability density |ψ|² of N electrons in the lowest Landau level.

5
0.0
0.0
Filling ν
1/3
Quasihole charge
e/3
Landau level
n=0
Plasma β
Laughlin wavefunction: ψ_m({zᵢ}) = ∏_{i<j}(zᵢ−zⱼ)ᵐ · exp(−∑|zᵢ|²/4l²_B)
Quasihole at z₀: ψ^QH = ∏ᵢ(zᵢ−z₀) · ψ_m — inserts one flux quantum, depletes charge e/m.
Plasma analogy: |ψ|² = exp(−β U) where U is 2D plasma energy → quasihole = charged impurity.