Quantum Hall Plateaus

σ_xy = νe²/h plateaus as Landau levels fill in a 2DEG

Magnetic field B Temperature kT/ℏω_c Disorder

Landau levels E_n = ℏω_c(n + ½) with ω_c = eB/m*. At each plateau the Hall conductance is exactly σ_xy = νe²/h — a topological invariant (Chern number). Disorder broadens Landau levels into bands of extended/localized states; the Hall plateau persists while the Fermi level lies in localized states. Edge states carry the current without backscattering.