Quantum Hall Effect — Chiral Edge States

Topological Edge Currents

In the quantum Hall effect, a 2D electron gas in a strong magnetic field develops quantized Hall conductance σxy = νe²/h, where ν is the filling factor (Landau level index).

The bulk is gapped (Landau levels), but chiral edge states carry current without dissipation. Chirality = one direction only, so backscattering is impossible — electrons skipping along the edge.

ν edge channels travel on one side, ν on the other (opposite direction). This visualization shows the cyclotron orbit skipping motion that builds up edge states.

σxy = νe²/h (exact, topological)
Chern number C = ν (filled Landau levels)
ωc = eB/m* (cyclotron frequency)