All approaches to RKKY interaction in graphene are equal, but some approaches are more equal than others

TL;DR

This paper demonstrates that two different Green's function methods for calculating RKKY interactions in graphene yield identical results, with the coordinate-imaginary time approach being more practical.

Contribution

It shows the equivalence of two calculation methods for RKKY interactions in graphene and advocates for the more convenient coordinate-imaginary time approach.

Findings

Both methods produce identical results.

No diverging integrals or cut-off procedures are needed.

Coordinate-imaginary time approach is more practical.

Abstract

We show explicitly that two approaches to calculations of RKKY interaction between two magnetic impurities in graphene based on Green's functions: one using coordinate--imaginary time representation, and the other using momentum--frequency representation, give exactly the same results and none of them has to operate with diverging integrals and implement the cut-off procedure. Together with this, we claim that the first approach is more convenient for the calculations than the second one.