Quantum Hall Quantized Cyclotron Entrance Channels

Abstract

Quantum Hall plateaus are entered via quantized cyclotron (QC) “cloud-chamber” orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both “canonical” and “magnetic” angular momentum components, which add together to form the invariant “kinematic” angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the un,l eigenstates un,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of ν = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.