Quantum Hall Effect

Landau levels · σ_xy = ne²/h · TKNN invariant

B = 5.0 T
n = 3.0
Γ = 1.0 meV
Physics: QHE discovered by von Klitzing (1980, Nobel 1985): Hall conductivity σ_xy = ne²/h quantized to 1 part in 10⁹ — used as resistance standard R_K = h/e² = 25,812.807 Ω. Landau levels: E_N = ℏω_c(N+½), ω_c = eB/m; each LL holds n_L = eB/h states per area. Filling factor ν = nh/eB. TKNN invariant (Thouless 1982): σ_xy = (e²/h)·C where C is an integer Chern number — topology guarantees quantization. Chiral edge states are topologically protected: backscattering requires traversing the bulk gap. FQHE: ν=1/3 (Laughlin 1983) — quasiparticles with fractional charge e/3.