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.