While calculating RKKY interaction in graphene no theorist should do a cut-off without cause

TL;DR

This paper compares two Green's function methods for calculating RKKY interactions in graphene, emphasizing the advantages of Matsubara Green's functions in coordinate-frequency and coordinate-imaginary time representations over zero temperature Green's functions.

Contribution

It introduces a coordinate-frequency representation for Matsubara Green's functions, enhancing the calculation of RKKY interactions in doped and gapped graphene.

Findings

Both approaches use convergent integrals, improving calculation reliability.

Coordinate-frequency representation simplifies analysis of doped and gapped graphene.

Matsubara Green's functions are advantageous over zero temperature Green's functions.

Abstract

In our previous work (E. Kogan, Phys. Rev. B 84, 115119 (2011)) we presented calculation of RKKY interaction between two magnetic impurities in graphene based on Matsubara Green's functions (MGF) in the coordinate -- imaginary time representation. Now we present the calculation based on MGF in the coordinate -- frequency representation. We claim that both approaches have an important advantage over those based on zero temperature Green's functions (ZTGF), which are very briefly reviewed in the beginning of the present work. The MGF approaches, in distinction to the ZTGF approaches, operate only with the convergent integrals from the start to the end of the calculation. The coordinate -- frequency representation for the MGF turns out to be as convenient as the coordinate -- imaginary time representation and allows to easily consider the cases of doped and gapped graphene.