Graphene's Half-Integer Quantum Hall Effect

Graphene's electrons are massless Dirac fermions, and in a magnetic field they form a Landau-level ladder that is spaced by a square root of the level index rather than evenly, with one level pinned exactly at zero energy and shared between electrons and holes. This simulator renders that ladder in 3D alongside a live Hall-conductivity staircase: sweep the magnetic field to spread the levels apart, and sweep a gate-tuned filling factor to move the Fermi level through them, watching the Hall conductivity lock onto graphene's signature ±4(n+½)e²/h plateau sequence — including the famous 2e²/h plateau exactly at the charge-neutrality point that first confirmed graphene hosts genuinely relativistic electrons.