Magnetic orbit to orbit interaction in a two-dimensional electron gas


The orbit to orbit magnetic interaction between electrons in a two-dimensional electron gas (2DEG) is considered. The orbit to orbit interaction is realized by constructing a Lorentz force law of a system of electrons accounting for both Coulomb electrostatic and Biot-Savart magnetostatic interactions, and external fields. From this, a generalized potential energy and Lagrangian is constructed. Using the calculated mechanical momentum, the effective Hamiltonian is expressed from the energy functon where a sufficient order of inverse speed of light is only considered. Using the Hartree approximation, the solution if the many-body Schrödinger equation with this Hamiltonian is approximated with an effective single-particle Schrödinger equation. From this the effective mean field Schrödinger equation is calculated. We look into the effects of the magnetic orbit-to-orbit interactiong through several forms of effective field potential energies.