Graphene Quantum Hall Effect (2D): Skipping Orbits & Edge Channels

This is the 2D counterpart of the graphene half-integer quantum Hall simulator. Rather than animating an abstract Landau-level ladder in 3D, it directly integrates the real-space motion of carriers confined to a graphene Hall bar: each carrier moves at graphene's fixed Fermi velocity and is deflected by the Lorentz force into an exact circular arc whose radius is set by the Fermi energy and field strength. Carriers far from the sample edge close into small loops — the localized, insulating bulk of a quantum Hall plateau — while carriers near an edge reflect off the boundary and hop forward instead of closing the loop, forming genuine chiral skipping orbits that carry current along the two edges in opposite directions. Live graphs alongside the trajectory view plot the quantized Hall resistance staircase and the Shubnikov–de Haas longitudinal-resistance oscillations that appear whenever a Landau level crosses the Fermi energy. Sweep the magnetic field and the gate-tuned filling factor to see the cyclotron radius, the number of conducting edge channels, and both resistance traces respond together.