Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells

TL;DR

This paper investigates how magnetic impurities interact indirectly in a 2D topological insulator based on CdTe/HgTe/CdTe quantum wells, revealing exponential decay, oscillations due to inversion asymmetry, and complex interaction structures.

Contribution

It provides a detailed analysis of the indirect exchange interaction in 2D topological insulators considering inversion asymmetry and energy gap effects, which was not previously characterized.

Findings

Interaction is exponentially suppressed with impurity distance.

Inversion asymmetry causes oscillations and additional non-rotationally invariant terms.

Interaction matrix has a complex structure with gap-dependent terms.

Abstract

We study indirect exchange interaction between magnetic impurities in the (001) CdTe/HgTe/CdTe symmetric quantum well. We consider low temperatures and the case of the chemical potential placed in the energy gap of the 2D quasiparticle spectrum. We find that the indirect exchange interaction is suppressed exponentially with the distance between magnetic impurities. The presence of inversion asymmetry results in oscillations of the indirect exchange interaction with the distance and generates additional terms which are non-invariant under rotations in the (001) plane. The indirect exchange interaction matrix has complicated structure with some terms proportional to the sign of the energy gap.