Generalized method of image dyons for quasi-two dimensional slabs with ordinary-topological insulator interfaces

TL;DR

This paper develops a comprehensive method to calculate magnetoelectric fields induced by electrostatic charges near topological insulator interfaces, extending previous models to asymmetric systems and various magnetization configurations.

Contribution

It provides generalized formulas for image dyons and magnetoelectric potentials in systems with multiple interfaces, applicable to diverse material configurations and external magnetizations.

Findings

Derived explicit formulas for image dyons in complex geometries

Enabled modeling of magnetoelectric fields in thin films and quantum wells

Provided computational tools for practical implementation

Abstract

Electrostatic charges near the interface bewteen topological (TI) and ordinary (OI) insulators induce magnetic fields in the medium that can be described through the so-called method of image dyons (electric charge - magnetic monopole pairs), the magnetoelectric extension of the method of image charges in classical electrostatics. Here, we provide the expressions for the image dyons and ensuing magnetoelectric potentials in a system comprised by two planar-parallel OI-TI interfaces conforming a finite-width slab. The obtained formulae extend earlier work in that they account for all different combinations of materials forming the slab and its surroundings, including asymmetric systems, as well as all possible combinations of external magnetization orientations on the interfaces. The equations are susceptible of implementation in simple computational codes, to be solved recurrently, in order to model magnetoelectric fields in topological quantum wells, thin films, or layers of two-dimensional materials. We exemplify this by calculating the magnetic fields induced by a point charge in nanometer-thick quantum wells, by means of a Mathematica code made available in repositories.