The role of orbit to orbit magnetic interaction in a two-dimensional electron gas in the quantum Hall regime

The orbit to orbit magnetic interaction between electrons in a quantum Hall system is considered. The standard method in the presence of scalar Coulomb interaction potential and external electromagnetic fields is to express the mechanical momentum as p + eA in the effective Hamiltonian. The orbit to orbit interaction is realized by constructing an effective system Hamiltonian possessing a magnetic interaction vector potential in the mechanical momentum. The resulting many-body Schrödinger equation with this Hamiltonian is solved to calculate the electron density and potential energy profiles.