An effective field analysis of magnetic orbit-to-orbit interactions in a two-dimensional electron gas

An effective field Schrödinger equation accounting for the effect of the magnetic orbit-to-orbit interaction between electrons in a two-dimensional electron gas (2DEG) is considered. This is formulated out from the effective single-particle equation using the Hartree approximation. As a specific example, a 2DEG in a Hall bar with rectangular geometry is considered, where such equation is reduced to a one-dimensional Schrödinger equation.