Current distribution in a two dimensional electron gas exposed to a perpendicular nonhomogeneous magnetic field of a chess configuration

TL;DR

This paper provides an exact analytical solution for the electric field and related physical quantities in a finite 2D electron system under a nonhomogeneous chess-pattern magnetic field, advancing understanding of magnetic interface effects.

Contribution

It introduces a conformal mapping method to derive an exact solution for electric field distribution in a nonuniform magnetic field with a chess configuration.

Findings

Exact formula for electric field distribution using Jacobi functions

Calculated current density and charge accumulation at magnetic interfaces

Analyzed magneto-resistance and Hall resistance in the system

Abstract

We have studied a finite two-dimensional electron system exposed to a normal nonhomogeneous magnetic field of a chess configuration. Using the conformal mapping method we obtain an exact analytical solution for the electric field distribution in terms of the Jacobi functions. The obtained formula is exploited to calculate the physical quantities of interest: the current density distribution, the linear density of charges accumulated along the magnetic interfaces, the magneto-resistance, and the Hall resistance.