Indirect exchange interaction between magnetic impurities in one-dimensional gapped helical states

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Spintronics

Background:

• One-dimensional gapped helical states host massive Dirac fermions.
• These states can emerge at the edges of 2D topological insulators with broken time-reversal symmetry.
• Understanding interactions mediated by these states is crucial for novel electronic devices.

Purpose of the Study:

• To theoretically investigate the indirect exchange interaction between magnetic impurities.
• To analyze the influence of 1D gapped helical states on this interaction.
• To characterize the different components of the exchange interaction and their dependencies.

Main Methods:

• Theoretical modeling of indirect exchange interaction.
• Analysis of massive Dirac fermions in helical states.
• Investigating Fermi level and energy gap effects on interaction terms.
• Considering electron-electron interactions.

Main Results:

• The indirect exchange interaction comprises Heisenberg, Dzyaloshinsky-Moriya, and Ising terms.
• Interaction terms decay exponentially within the bandgap, with the Dzyaloshinsky-Moriya term being minimal.
• Outside the bandgap, helical states alter oscillatory behaviors, decreasing oscillation periods near band edges.
• The out-of-plane Ising term vanishes in zero-gap structures and its amplitude varies with energy gap and Fermi energy.

Conclusions:

• The nature and strength of magnetic impurity interactions are significantly modified by 1D gapped helical states.
• The findings offer insights into controlling magnetic interactions in topological materials.
• This work provides a theoretical foundation for spintronic applications utilizing topological edge states.