Quantum Hall Edge States

This simulator renders a two-dimensional electron gas confined to a rectangular Hall bar under a strong perpendicular magnetic field, integrating each electron's real cyclotron motion (velocity rotating at ω_c = eB/m*, specularly reflecting off the hard walls) rather than faking the trajectories. The result is the genuine mechanism behind the integer quantum Hall effect: bulk electrons trace closed loops that carry no net current, while electrons whose orbits touch the boundary become chiral "skipping orbits" that hop one-way around the entire perimeter, forming a dissipationless edge current. Sliders for magnetic field and areal density drive live readouts of the cyclotron frequency, the Landau-level energy gap, and the filling factor ν = nh/(eB); a disorder toggle pins bulk orbits to impurities to show why the Hall conductance locks onto flat, precisely quantized plateaus instead of jumping discontinuously.