Dissipationless Topological Edge Current

Chiral Edge States — Robust Against Disorder — Quantized Hall Conductance
Band structure + chiral edge states
Real-space transport (click to add disorder)
EF = 0.00 Δ
Δ = 0.80 t
W = 0.00
N = 16 sites
Hall conductance:
σ_xy = C·e²/h
Chern number:
C = (1/2π)∫BZ Ω_k d²k
Berry curvature:
Ω_k = ∇_k × A_k
Bulk-edge correspondence:
# edge modes = |C|
Edge dispersion:
E_edge(k) ≈ v_F·(k − k₀)
Topological protection:
No backscattering
unless gap closes!
Chiral edge states in a topological insulator propagate in one direction only along each boundary. Backscattering requires crossing the bulk gap — topologically forbidden. The Hall conductance σ_xy = Ce²/h is quantized to integer C (Chern number), a topological invariant. This is dissipationless transport: ρ_xx = 0, ρ_xy = h/(Ce²).